Question

Let X be exponential random variable with λ = 1. (a) Define Y = √ X....

Let X be exponential random variable with λ = 1.
(a) Define Y = √ X. Specify the support of Y and find its density.

(b)Define Z = X^2 + 2X. Specify the support of Z and find its density.

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Answer #1

An Exponential (x=1). Por of his fre) = leon ocaco (a) Y = √x O x 200 = 0c yoo Clearly :.= support of 4 = {4: 0 ky coo} Now,Por of y. fyly) = f(x²). I dal 10 Ly 200 O, O-W. 24 e 0,0-W. (6) Z=x²+2x. OLALA» x²+2x>0 and Now, & OLZLX. x²+2x La .: Suppor

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