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- The continuous random variable Y has the following pdf: 1- y?, 0A bank operates both a drive-up facility and a walk-up window. On a randomly selected day, let X be the proportion of time that the drive-up facility is in use (at least one customer is being served or waiting to be served) and Y be the proportion of time that the walk-up window is in use. The joint PDF is ... fxy (x, y) = 5 (x + y²) • What is the probability that neither window is busy more than one-quarter of the time? • What is f(X)? • What is fy(y)?4. Let X be a random variable with cumulative distribution function given by: F(r) = 1 – e-Az. Find the probability density function and so the expected value of variable X.Let X be a random variable with CDF x > 1 Fx(x) = 0 < x < 1 %3D x < 0 a. What kind of random variable is X: discrete, continuous, or mixed? b. Find the PDF of X, fx(x). c. Find E(ex).Consider the random variable X with PDF (known as Cauchy distri- bution) f(x) = 7 - 00A random variable has the following probability density function (pdf), f(x) = { 0(2x - 2²) 0≤x≤2 0 otherwise Determine E(3X + 4)..Recommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSONA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON