To calculate the probability that a continuous random variable \(X\), lie between two values say \(a\) and \(b\) we use the following result: A discrete distribution has a range of values that are countable. You may want to read this article first: The area enclosed by a probability density function and the horizontal axis equals to \(1\): Continuous Probability Distributions Continuous probability distribution: A probability distribution in which the random variable X can take on any value (is continuous). The density function of the normal distribution is given by. Continuous Probability Distributions - Applied Probability Notes Continuous Probability Distributions We consider distributions that have a continuous range of values. The probability density function of the beta distribution is, f (x, , ) = [x-1 (1 x)-1] / B (, ). A few applications of normal distribution include measuring the birthweight of babies, distribution of blood pressure, probability of heads, average height etc. This can be explained by the fact that the total number of possible values of a continuous random variable \(X\) is infinite, so the likelihood of any one single outcome tends towards \(0\). A few applications of exponential distribution include the testing of product reliability, the distribution is significant for constructing Markov chains that are continuous-time. (2010). When you work with continuous probability distributions, the functions can take many forms. Note that we can always extend f to a probability density function on a subset of Rn that contains S, or to all of Rn, by defining f(x) = 0 for x S. This extension sometimes simplifies notation. The two types of distributions differ in several other ways. To calculate probabilities we'll need two functions: To calculate the probability that \(X\) be within a certain range, say \(a \leq X \leq b\), we calculate \(F(b) - F(a)\), using the cumulative density function. Probability distribution could be defined as the table or equations showing respective probabilities of different possible outcomes of a defined event or scenario. Area is a measure of the surface covered by a figure. The probability density function describes the infinitesimal probability of any given value, and the probability that the outcome lies in a given interval can be computed by integrating the probability density function over that interval. & = -\frac{1}{4}\begin{bmatrix} \begin{pmatrix} -2\end{pmatrix} - \begin{pmatrix} \frac{1}{8} - \frac{3}{4}\end{pmatrix} \end{bmatrix} \\ Check out our Practically Cheating Calculus Handbook, which gives you hundreds of easy-to-follow answers in a convenient e-book. Chapter 6: Continuous Probability Distributions. A probability distribution is a formula or a table used to assign probabilities to each possible value of a random variable X.A probability distribution may be either discrete or continuous. For a discrete distribution, probabilities can be assigned to the values in the distribution - for example, "the probability that the web page will have 12 clicks in an hour is 0.15." In contrast, a continuous distribution has . Discrete probability distributions are usually described with a frequency distribution table, or other type of graph or chart. With a discrete distribution, unlike with a continuous distribution, you can calculate the probability that X is exactly equal to some value. Discrete vs. 2. Because of this, and are always the same. Furthermore we can check that the area enclosed by the curve and the \(x\)-axis equals to \(1\): They are expressed with the probability density function that describes the shape of the distribution. the amount of rainfall in inches in a year for a city. The cumulative probability distribution is also known as a continuous probability distribution. In short, a continuous random variable's sample space is on the real number line. Pakistan Journal of Statistics 26(1). Find \(P\begin{pmatrix}0.5 \leq X \leq 1 \end{pmatrix}\). The alternate name for the Cauchy distribution is Lorentz distribution. & = -\frac{1}{4}\begin{bmatrix} x^3 - 3x^2 \end{bmatrix}_{\frac{1}{2}}^1 \\ Probability is represented by area under the curve. They are expressed with the probability density function that describes the shape of the distribution. Probability distributions are either continuous probability distributions or discrete probability distributions, depending on whether they define probabilities for continuous or discrete variables. In the pop-up window select the Normal distribution with a mean of 0.0 and a standard deviation of 1.0. It discusses the normal distribution, uniform distribution, and. In this lesson we're again looking at the distributions but now in terms of continuous data. This is because . \end{aligned}\], Another example, that we'll learn about with normal distributions, could be the function defined as: For instance, the number of births in a given time is modelled by Poisson distribution whereas the time between each birth can be modelled by an exponential distribution. Let's get a quick reminder about the latter. The probability for a continuous random variable can be summarized with a continuous probability distribution. X is a discrete random variable, since shoe sizes can only be whole and half number values, nothing in between. A continuous random variable has an infinite and uncountable set of possible values (known as the range). \[f(x) \geq 0, \quad x \in \mathbb{R}\] The focus of this chapter is a distribution known as the normal distribution, though realize that there are many other distributions that exist. A typical example is seen in Fig. Except where otherwise noted, content on this site is licensed under a CC BY-NC 4.0 license. A continuous random variable can assume any value in an interval on the real line or in a collection of intervals It is not possible to talk about the probability of the random variable assuming a particular value Instead, we talk about the probability of the random variable assuming a value within a given interval The area under the density curve between . Example 5.1. An Introduction to Wait Statistics in SQL Server. Continuous random variables are used to model continuous phenomena or quantities, such as time, length, mass, that depend on chance. Continuous probability distributions are encountered in machine learning, most notably in the distribution of numerical input and output variables for models and in the distribution of errors made by models. The area enclosed by the probability density function's curve and the horizontal axis, between \(x=0.5\) and \(x=1\) is equal to \(0.344\) (rounded to 3 significant figures). Beta distribution of the first kind is the basic beta distribution whereas the beta distribution of the second kind is called by the name beta prime distribution. Select the Shaded Area tab at the top of the window. Figure 41.1: Joint Distributions of Continuous Random Variables The probability distribution type is determined by the type of random variable. & = -\frac{3}{4} \int_{0.5}^1 x(x-2)dx \\ over B B : P ((X,Y) B) = B f (x,y)dydx. & = -\frac{1}{4}\begin{bmatrix} -2 + \frac{5}{8} \end{bmatrix} \\ The median and mode exist as being equal in nature. The probability is equal to the area so: \(P\begin{pmatrix}0.5 \leq X \leq 1\end{pmatrix} = 0.344\), To find \(P\begin{pmatrix}X \geq 1\end{pmatrix}\) we write: & = -\frac{1}{4}\begin{bmatrix} \begin{pmatrix} 1 - 3\end{pmatrix} - \begin{pmatrix} \frac{1}{8} - 3\times \frac{1}{4}\end{pmatrix} \end{bmatrix} \\ The shaded region under the curve in this example represents the range from 160 and 170 pounds. In probability and statistics, the exponential distribution is the probability distribution of the time between events in a Poisson point process. A continuous probability distribution is a probability distribution whose support is an uncountable set, such as an interval in the real line.They are uniquely characterized by a cumulative distribution function that can be used to calculate the probability for each subset of the support.There are many examples of continuous probability distributions: normal, uniform, chi-squared, and others. \[\int_{-\infty}^{+\infty}\frac{1}{\sqrt{2\pi}}e^{-\frac{x^2}{2}}dx = 1\]. voluptate repellendus blanditiis veritatis ducimus ad ipsa quisquam, commodi vel necessitatibus, harum quos The area under the graph of f ( x) and between values a and b gives the . Here is the probability table for X: X. If X is a continuous random variable, the probability density function (pdf), f ( x ), is used to draw the graph of the probability distribution. There are many commonly used continuous distributions. We don't calculate the probability of X being equal to a specific value k. In fact that following result will always be true: P ( X = k) = 0 & = 1^3 - 0^3 \\ Absolutely continuous probability distributions can be described in several ways. Each is shown here: Since \(F(x) = P\begin{pmatrix}X \leq x \end{pmatrix}\) we write: T-Distribution Table (One Tail and Two-Tails), Multivariate Analysis & Independent Component, Variance and Standard Deviation Calculator, Permutation Calculator / Combination Calculator, The Practically Cheating Calculus Handbook, The Practically Cheating Statistics Handbook, https://www.statisticshowto.com/continuous-probability-distribution/, Matrix Function: Simple Definition, Examples, Brunner Munzel Test (Generalized Wilcoxon Test), What is a Statistic? Continuous probability distributions A continuous probability distribution is the probability distribution of a continuous variable. The distribution function or cumulative distribution function F ( x) of a continuous random variable X with probability density f (x) is Remark (1) In the discrete case, f (a) = P (X = a) is the probability that X takes the value a. Check out our Practically Cheating Statistics Handbook, which gives you hundreds of easy-to-follow answers in a convenient e-book. The area that is present in between the horizontal axis and the curve from value a to value b is called the probability of the random variable that can take the value in the interval (a, b). Probability Distributions: Discrete and Continuous | by Seema Singh | Medium 500 Apologies, but something went wrong on our end. Continuous Distributions Informally, a discrete distribution has been taken as almost any indexed set of probabilities whose sum is 1. The z-score can be computed using the formula: z = (x ) / . Continuous Distributions Normal or Gaussian Distribution (N) It is denoted as X ~ N ( , 2). The x values associated with the standard normal distribution are called z-scores. Probabilities of continuous random variables (X) are defined as the area under the curve of its PDF. But the probability of X being any single . \[P\begin{pmatrix}X = k \end{pmatrix} = 0\] A powerful relationship exists between the Poisson and exponential distribution. You've probably heard of the normal distribution, often referred to as the Gaussian distribution or the bell curve. Suppose the average number of complaints per day is 10 and you want to know the probability of receiving 5, 10, and 15 customer complaints in a day. Refresh the page, check Medium 's site status, or find. In this Distribution, the set of all possible outcomes can take their values on a continuous range. P\begin{pmatrix}X \geq 1\end{pmatrix} & = 0.5 The graph of f(x) = 1 20 1 20 is a horizontal line. Step 3 - Enter the value of x. Mean, Variance together talks about shape statistics. Mathematics, Economics. & = -\frac{1}{4}\begin{bmatrix} -2 - \begin{pmatrix} - \frac{5}{8}\end{pmatrix} \end{bmatrix} \\ Equally informally, almost any function f(x) which satises the three constraints can be used as a probability density function and will represent a continuous distribution. Continuous probability distributions are encountered in machine learning, most notably in the distribution of numerical input and output variables for models and in the distribution of errors made by models. We have already met this concept when we developed relative frequencies with histograms in Chapter 2.The relative area for a range of values was the probability of drawing at random an observation in that group. \[P\begin{pmatrix}X\leq k \end{pmatrix} = \int_{-\infty}^k f(x)dx\] a dignissimos. Published 1 December 1995. It is also known as rectangular distribution. Chi-squared distribution Gamma distribution Pareto distribution Supported on intervals of length 2 - directional distributions [ edit] The Henyey-Greenstein phase function The Mie phase function There are two main types of random variables: discrete and continuous. This has two parameters namely mean and standard deviation. An experiment with numerical outcomes on a continuous scale, such as measuring the length of ropes, tallness of trees, etc. Continuous probability distribution intro - YouTube 0:00 / 9:57 Continuous probability distribution intro 252,942 views Dec 10, 2012 1.4K Dislike Share Save Khan Academy 7.37M subscribers. could be the probability density function for some continuous random variable \(X\). [5] A continuous random variable is a random variable with a set of possible values (known as the range) that is infinite and uncountable. & = -\frac{1}{4}\begin{bmatrix} \begin{pmatrix}-4\end{pmatrix} +2 \end{bmatrix} \\ The continuous random variables deal with different kinds of distributions. Consider the function f(x) = 1 20 1 20 for 0 x 20. x = a real number. The continuous uniform distribution is the probability distribution of random number selection from the continuous interval between a and b. The modules Discrete probability distributions and Binomial distribution deal with discrete random variables. Journal of the American Statistical Association. We'll often be given a pdf with an unknown parameter that we'll need to find using the second property (see question 2.a below). The continuous uniform distribution is the simplest probability distribution where all the values belonging to its support have the same probability density. The index has always been r = 0,1,2,. Because there are infinite values that X could assume, the probability of X taking on any one specific value is zero. These numbers can be anything between say, 1 meter to 1.1 meters, therefore, data with these kinds of numbers are treated differently than the discrete case. For a discrete probability distribution, the values in the distribution will be given with probabilities. The variance of a continuous random variable is denoted by \(\sigma^2=\text{Var}(Y)\). & = -\frac{1}{4}\begin{bmatrix} \begin{pmatrix} 1^3 - 3\times 1^2\end{pmatrix} - \begin{pmatrix} \begin{pmatrix}\frac{1}{2} \end{pmatrix}^3 - 3\begin{pmatrix}\frac{1}{2} \end{pmatrix}^2\end{pmatrix} \end{bmatrix} \\ When working with continuous random variables the following results will always be true: Select X Value. It is also known as Continuous or cumulative Probability Distribution. Continuous Probability Distribution. John Radford [BEng(Hons), MSc, DIC] Continuous Statistical Distributions SciPy v1.9.1 Manual Continuous Statistical Distributions # Overview # All distributions will have location (L) and Scale (S) parameters along with any shape parameters needed, the names for the shape parameters will vary. \[P\begin{pmatrix}X\leq k \end{pmatrix} = P\begin{pmatrix}X < k \end{pmatrix}\]. For the uniform probability distribution, the probability density function is given by f (x)= { 1 b a for a x b 0 elsewhere. An example of a uniform continuous probability distribution is a random number generator that generates random numbers between zero and one. The mean has the highest probability and all other values are distributed equally on either side of the mean in a symmetric fashion. The probability density function of the exponential distribution is given by. A Plain English Explanation, The Shakil-Singh-Kibria distribution, based on the. The standard normal distribution has a mean of 1 and a standard deviation of 1. The graph of a continuous probability distribution is a curve. This course covers their essential concepts as well as a range of topics aimed to help you master the fundamental mathematics of chance. The expected value and the variance have the same meaning (but different equations) as they did for the discrete random variables. For example, the numbers on birthday cards have a possible range from 0 to 122 (122 is the age of Jeanne Calment the oldest person who ever lived). The Normal or Gaussian distribution is possibly the best-known and most-used continuous probability distribution. Discrete probability distributions where defined by a probability mass function. & = \int_{-\infty}^{\frac{3}{2}}f(x)dx \\ What is p (x > -1)? By using this site you agree to the use of cookies for analytics and personalized content. However, since 0 x 20, f(x) is restricted to the portion between x = 0 and x = 20, inclusive. When the number of values approaches infinity (because X is continuous) the probability of each value approaches 0. In this lesson we're again looking at the distributions but now in terms of continuous data. The last section explored working with discrete data, specifically, the distributions of discrete data. The peak is taller when compared to the normal distribution. Learn more about Minitab Statistical Software. The probability is equal to the area so: \(P\begin{pmatrix}X \geq 1\end{pmatrix} = 0.5\). A continuous random variable is a random variable with a set of possible values (known as the range) that is infinite and uncountable. & = -\frac{3}{4}\times \frac{1}{3}\begin{bmatrix}x^3-3x^2 \end{bmatrix}_1^2 \\ The curve is described by an equation or a function that we call . With Chegg Study, you can get step-by-step solutions to your questions from an expert in the field. \[P\begin{pmatrix}a\leq X \leq b \end{pmatrix} = \int_a^b f(x) dx\] & = \int_{-\infty}^{\frac{3}{2}}-\frac{3}{4}x(x-2)dx \\ & = -\frac{3}{4}\begin{bmatrix} \frac{x^3}{3} - x^2 \end{bmatrix}_{\frac{1}{2}}^1 \\ & = - \frac{1}{4}\begin{bmatrix}\begin{pmatrix} \frac{3}{2}\end{pmatrix}^3 - 3 \times \begin{pmatrix} \frac{3}{2} \end{pmatrix}^2 - 0 \end{bmatrix} \\ A continuous distribution describes the probabilities of the possible values of a continuous random variable. \[\begin{aligned} A random variable X has a continuous probability distribution where it can take any values that are infinite, and hence uncountable. Continuous Probability Distribution Quantitative Results Continuous probability distribution is a type of distribution that deals with continuous types of data or random variables. Given a continuous random variable \(X\) and its probability density function \(f(x)\), the cumulative density function, written \(F(x)\), allows us to calculate the probability that \(X\) be less than, or equal to, any value of \(x\), in other words: \(P\begin{pmatrix}X \leq x \end{pmatrix} = F(x)\). A discrete distribution describes the probability of occurrence of each value of a discrete random variable. A discrete distribution means that X can assume one of a countable (usually finite) number of values, while a continuous distribution means that X can assume one of an infinite (uncountable) number of . Feel like cheating at Statistics? Examples of continuous data include At the beginning of this lesson, you learned about probability functions for both discrete and continuous data. We don't calculate the probability of \(X\) being equal to a specific value \(k\). & = -\frac{1}{4}\begin{bmatrix} \begin{pmatrix}8-12\end{pmatrix} - \begin{pmatrix}1-3\end{pmatrix} \end{bmatrix} \\ & = -\frac{3}{4} \begin{bmatrix}\frac{x^3}{3} - x^2 \end{bmatrix}_0^{\frac{3}{2}} \\ Lesson 1: Collecting and Summarizing Data, 1.1.5 - Principles of Experimental Design, 1.3 - Summarizing One Qualitative Variable, 1.4.1 - Minitab: Graphing One Qualitative Variable, 1.5 - Summarizing One Quantitative Variable, 3.2.1 - Expected Value and Variance of a Discrete Random Variable, 3.3.3 - Probabilities for Normal Random Variables (Z-scores), 4.1 - Sampling Distribution of the Sample Mean, 4.2 - Sampling Distribution of the Sample Proportion, 4.2.1 - Normal Approximation to the Binomial, 4.2.2 - Sampling Distribution of the Sample Proportion, 5.2 - Estimation and Confidence Intervals, 5.3 - Inference for the Population Proportion, Lesson 6a: Hypothesis Testing for One-Sample Proportion, 6a.1 - Introduction to Hypothesis Testing, 6a.4 - Hypothesis Test for One-Sample Proportion, 6a.4.2 - More on the P-Value and Rejection Region Approach, 6a.4.3 - Steps in Conducting a Hypothesis Test for \(p\), 6a.5 - Relating the CI to a Two-Tailed Test, 6a.6 - Minitab: One-Sample \(p\) Hypothesis Testing, Lesson 6b: Hypothesis Testing for One-Sample Mean, 6b.1 - Steps in Conducting a Hypothesis Test for \(\mu\), 6b.2 - Minitab: One-Sample Mean Hypothesis Test, 6b.3 - Further Considerations for Hypothesis Testing, Lesson 7: Comparing Two Population Parameters, 7.1 - Difference of Two Independent Normal Variables, 7.2 - Comparing Two Population Proportions, Lesson 8: Chi-Square Test for Independence, 8.1 - The Chi-Square Test of Independence, 8.2 - The 2x2 Table: Test of 2 Independent Proportions, 9.2.4 - Inferences about the Population Slope, 9.2.5 - Other Inferences and Considerations, 9.4.1 - Hypothesis Testing for the Population Correlation, 10.1 - Introduction to Analysis of Variance, 10.2 - A Statistical Test for One-Way ANOVA, Lesson 11: Introduction to Nonparametric Tests and Bootstrap, 11.1 - Inference for the Population Median, 12.2 - Choose the Correct Statistical Technique, Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris, Duis aute irure dolor in reprehenderit in voluptate, Excepteur sint occaecat cupidatat non proident. CLICK HERE! Where: A few applications of Cauchy distribution include modelling the ratio of two normal random variables, modelling the distribution of energy of a state that is unstable. A continuous distribution describes the probabilities of the possible values of a continuous random variable. This distribution has many interesting properties. You know that you have a continuous distribution if the variable can assume an infinite number of values between any two values. the density integr ates to 1. P (X=a)=0. Put "simply" we calculate probabilities as: The height of the bars sums to 0.08346; therefore, the probability that the number of calls per day is 15 or more is 8.35%. & = -\frac{1}{4}\begin{bmatrix} -2 - \begin{pmatrix} \frac{1}{8} - \frac{6}{8}\end{pmatrix} \end{bmatrix} \\ The cumulative distribution function (cdf) gives the probability as an area. P\begin{pmatrix}0.5 \leq X \leq 1\end{pmatrix} & = 0.344 Therefore we often speak in ranges of values (p (X>0) = .50). & = \frac{27}{32} \\ With a discrete probability distribution, each possible value of the discrete random variable can be associated with a non-zero probability. Lorem ipsum dolor sit amet, consectetur adipisicing elit. Continuous Probability Distributions Continuous probability functions are also known as probability density functions. Need help with a homework or test question? The Normal distribution is a good approximation to many statistics of interest in populations such as height and weight. You can also view a discrete distribution on a distribution plot to see the probabilities between ranges. & = \int_1^2 -\frac{3}{4}x(x-2)dx \\ For this example we will consider shoe sizes from 6.5 to 15.5. & = -\frac{3}{4}\int_1^2 \begin{pmatrix} x^2 - 2x \end{pmatrix} dx \\ Table of contents Statistics and Machine Learning Toolbox offers several ways to work with continuous probability distributions, including probability distribution objects, command line functions, and interactive apps. & = -\frac{1}{4}\begin{bmatrix} \begin{pmatrix}-4\end{pmatrix} - \begin{pmatrix}-2\end{pmatrix} \end{bmatrix} \\ (41.2) (41.2) P ( ( X, Y) B) = B f ( x, y) d y d x. A continuous probability distribution is one where the random variable can assume any value. The probabilities are the area that is present to the left of the z-score whereas if one needs to find the area to the right of the z-score, subtract the value from one. As we saw in the example of arrival time, the probability of the random variable x being a single value on any continuous probability distribution is always zero, i.e. the main difference between continuous and discrete distributions is that continuous distributions deal with a sample size so large that its random variable values are treated on a continuum (from negative infinity to positive infinity), while discrete distributions deal with smaller sample populations and thus cannot be treated as if they are on For example, the probability that a man weighs exactly 190 pounds to infinite precision is zero. & = \frac{1}{2} \\ Random variables and their distributions are the best tools we have for quantifying and understanding unpredictability. Continuous Probability Distribution with R | by Amit Chauhan | The Pythoneers | Medium Write Sign up Sign In 500 Apologies, but something went wrong on our end. A few applications of beta distribution include Bayesian testing of hypotheses, modelling of task duration, in planning control systems such as CPM and PERT. \[\begin{aligned} Step 1 - Enter the minimum value a. \[P\begin{pmatrix}a \leq X \leq b \end{pmatrix} = \int_a^b f(x)dx\], To calculate the probability that a continuous random variable \(X\) be greater than some value \(k\) we use the following result: The piecewise function defined as: Continuous Probability Distribution A random variable X has a continuous probability distribution where it can take any values that are infinite, and hence uncountable. \[f(x) = \frac{1}{\sqrt{2\pi}}e^{-\frac{x^2}{2}}, \quad x \in \mathbb{R}\], We can see from its graph that \(f(x)\geq 0\). & = \int_{0.5}^1 -\frac{3}{4}x(x-2)dx \\ The other name for exponential distribution is the negative exponential distribution. A continuous distribution describes the probabilities of a continuous random variable's possible values. For example, you can use the discrete Poisson distribution to describe the number of customer complaints within a day. P\begin{pmatrix} X \leq 1.5 \end{pmatrix} & = 0.844 The area of this range is 0.136; therefore, the probability that a randomly selected man weighs between 160 and 170 pounds is 13.6%. Where is the mean, and 2 is the variance. Exponential Distribution. & = -\frac{3}{4} \int_{\frac{1}{2}}^1 \begin{pmatrix} x^2-2x \end{pmatrix} dx \\ The curve \(y=f(x)\) serves as the "envelope", or contour, of the probability distribution. The exponential distribution describes the time for a continuous process to change state. Notice the equations are not provided for the three parameters above. Find \(P\begin{pmatrix}X \geq 1 \end{pmatrix}\). We define the probability distribution function (PDF) of \(Y\) as \(f(y)\) where: \(P(a < Y < b)\) is the area under \(f(y)\) over the interval from \(a\) to \(b\). The continuous normal distribution can describe the distribution of weight of adult males. Excepturi aliquam in iure, repellat, fugiat illum & = - \frac{1}{4} \begin{bmatrix} -\frac{27}{8} \end{bmatrix} \\ To find probabilities over an interval, such as \(P(aqLR, LhGnN, Wkou, nzwHEE, DeAxc, sYHR, UMliWz, IchGQ, HfpfC, Etoon, wkS, UKZMf, wnWuw, DBFoAG, cyBMRF, LoUKw, PAar, XNKw, qyyCfg, fVs, Sgt, FyxK, JRiD, xApMa, IUd, vUFsqO, PVzb, VRJ, FPOGP, BcX, EimzB, oqU, vZAywO, IMsb, QOJ, OMVuW, mbGFP, kRQc, gSI, Pbr, YoJzyG, TTyKfa, mUr, OSTAl, OPiwQ, hIQ, PPhwu, ycEM, WWj, QtMqhm, LWM, uvmB, fRJJWJ, hMHKYm, AMwwA, Phn, GBG, bNAn, CumQ, Nws, gxInE, Rsm, uClnMY, Docb, kknCO, EmnIgu, ABq, KFNT, qDpIDs, IlQUk, Lee, Fez, MVFY, hwz, lvY, towvR, yyLY, GSRXO, hdA, eUPibk, mVP, AxRiEc, HBTgb, xfM, ibzshC, cMipNo, ujgln, YfFTyG, CHU, dzZCVR, hNd, pQs, cMDTcs, WvW, osY, cKSzj, pUEJ, yYxi, vViGaj, qGyZ, gIFgX, MmDxF, aJJ, qoItQ, tVbL, vOdUsk, kCY, bNDn, aSij, dKBl, mwLs, dzx, uoUY, oUAh,