3.20 Let the random variable X have the pdf f(x) : 0 < x < o. e V2T (a) Find the mean and variance of X. (This distribution is sometimes called a fo normal.)

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Section 3.7
EXERCISES
3.20 Let the random variable X have the pdf
/2
f (x) =
V2T
0 <x < o.
(a) Find the mean and variance of X. (This distribution is sometimes called a fc
normal.)
(b) If X has the folded normal distribution, find the transformation g(X) = Y
values of a and B so thatY
%3D
gamma(a, 6).
3.21 Write the integral that would define the mgf of the pdf
Transcribed Image Text:Section 3.7 EXERCISES 3.20 Let the random variable X have the pdf /2 f (x) = V2T 0 <x < o. (a) Find the mean and variance of X. (This distribution is sometimes called a fc normal.) (b) If X has the folded normal distribution, find the transformation g(X) = Y values of a and B so thatY %3D gamma(a, 6). 3.21 Write the integral that would define the mgf of the pdf
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