Let X be a random variable taking values in (0,∞) with proba-bility density functionfX(u) = 5e^−5u, u > 0.Let Y = X2 Total marks 8 . Find the probability density function of Y .
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Let X be a random variable taking values in (0,∞) with proba-
bility density function
fX(u) = 5e^−5u, u > 0.
Let Y = X2 Total marks 8 . Find the probability density function of Y .
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- Let Y be a random variable with pdf f(y)= (1/18)(y^3−1) for 1<y<3.(a) Calculate P (Y > 2.5).(b) Calculate the variance of Y .2. Let X be a Chi-squared random variable with density function fx(x) = exp (-;), a x > 0. Suppose Y is independent of, and has the same distribution as, X. (a) Let Z = VX. Show that the density function of Z is given by Sale) = 2a exp (-) z > 0. Hence state the value of a.Let X be a continuous random variable with probability density function f(x) otherwise 5x x > 1 = Let U = 1 - X for X > 1. Find P{U > }}.