# Question: Suppose X is uniformly distributed over a a where

Suppose X is uniformly distributed over (– a, a), where a is some positive constant. Find the PDF of Y= X2.

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Suppose X is a random variable with an exponential PDF of the form fX(x) = 2e– 2xu(x). A new random variable is created according to the transformation Y = 1 – X. (a) Find the domain for X and Y. (b) Find fY(y) In each of the following cases, find the value of the parameter a which causes the indicated random variable to have a mean value of 10. (a) (b) (c) A pair of random variables has a joint PDF specified by (a) Find (X > 2, Y < 0). (b) Find Pr (0 < X < 2, | Y + 1| > 2. (c) Find Hint: Set up the appropriate double integral and then use the change of variables: u = x – ...Consider again the random variables of exercise 5.12 that are uniformly distributed over an ellipse. (a) Find the conditional PDFs, fX|Y (x| y) and fY|X (y|x). (b) Find f X|Y > 1(x). (c) Find fY |{|X| < 1}. Suppose two random variables are related by Y = a X2 and assume that is symmetric about the origin. Show that ρ X, Y = 0.Post your question