5. (16pts 4,4,4,4) Answer the following questions in regards to transformations. (a) Let the random variable X have a pd

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5 16pts 4 4 4 4 Answer The Following Questions In Regards To Transformations A Let The Random Variable X Have A Pd 1 (27.33 KiB) Viewed 32 times

5. (16pts 4,4,4,4) Answer the following questions in regards to transformations. (a) Let the random variable X have a pdf of f(x) = 1 for 0 <<<1. Find the distribution of Y = 3(-In(X))& (b) Suppose we have a continuous random variable X whose distribution is symmetric about 0. That is fx(a) = fx(-a) for all acR+. Show that the transformation Y = |x|has density, fy() = 2x(y) for random variables who are symmetric about 0. (C) If Y is a linear transformation, Y =aX+, of a discrete random variable X which takes values on x = {0, 1, 2, 3, 4), derive a general form for the pmf of Y. (a) In a more general setting of part c, let y be a linear transformation of any random variable X, Y = ax + b. Show that if we set b = a, E(Y) = a g? +(4+1) 2