Question

Let X have density fX(x) = C/ sqrt(x), 0 < x < 1 (a) Find the...

Let X have density fX(x) = C/ sqrt(x), 0 < x < 1

(a) Find the cumulative distribution FY (y) and probability density function fY (y) of Y = X(1 − X).

(b) Find probability density function fZ(z) of Z = X1/4 .

SHOW ALL STEPS OF WORKING OUT CLEARLY PLEASE.THANKS!

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

a) Please check the question. It is supposed to be X/(1-X) as per my knowledge since here X follows Beta1(1/2, 1). Then Y would follow Beta2(1/2,1)

b) i have assumed the transformation Z=X/4 since there is no X1

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