I would appreciate if anyone could help with this question. It is from Probability and Statistics with Applications: A Problem Solving Text Asimow and Mawell

8-3

Suppose that the random variable X has an exponential distribution with mean one. Let the random variable Y= sqrt (X)

(a) Find the probability density function for Y.

(b) Find the expected value for Y.

For part (a) I got the density function for Y: f(y)= (density function for X)*(dx/dy) = e^-x * 2y= 2ye^(-y^2)

Using that answer I attempted to solve part (b) by doing the integral from 0 to infinity of y*f(y). But I cannot figure out a solution using integration tables or integration by parts. I suspect I've made an error in the density function of Y.

8-3

Suppose that the random variable X has an exponential distribution with mean one. Let the random variable Y= sqrt (X)

(a) Find the probability density function for Y.

(b) Find the expected value for Y.

For part (a) I got the density function for Y: f(y)= (density function for X)*(dx/dy) = e^-x * 2y= 2ye^(-y^2)

Using that answer I attempted to solve part (b) by doing the integral from 0 to infinity of y*f(y). But I cannot figure out a solution using integration tables or integration by parts. I suspect I've made an error in the density function of Y.

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