Consider an exponentially distributed random variable X with pdf f(x) = 2e−2x for x ≥ 0....

Question

Question

Consider an exponentially distributed random variable X with pdf f(x) = 2e−2x for x ≥ 0. Let Y = √X.

a. Find the cdf for Y.

b. Find the pdf for Y.

c. Find E[Y]. If you want to skip a difficult integration by parts, make a substitution and look for a Gamma

pdf.

d. This Y is actually a commonly used continuous distribution. Can you name it and identify its parameters?

e. Suppose that X is exponentially distributed with mean 1/λ. Let Y = X1n. Then we can read

this as Y is the nth root of an exponential random variable. What sort of distribution does Y follow and what are its parameters?

Answer 1

Answer #1

Answer 2

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