Question 3 Let X~ Gamma(a, B) be a Gamma random variable. That is, fx (2) = 0, I<0. Consider the reciprocal variable, Y = x. %3D (a) Consider the cumulative distribution function (cdf) ofY, Fy(y). Write Fy (y) in terms of the cdf of X, Fx- (b) Verify that the cdf you derived above is a valid cdf. (c) Consider the probability density function (pdf) of Y, fy(y). Show that the pdf of Y is, y> 0; fy (y) = {ay %3D y< 0. (d) Verify that the pdf above is a valid pdf.

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Chapter1: Starting With Matlab
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please send solution for part c and d
Question 3
Let X~
Gamma(a, B) be a Gamma random variable. That is,
>0;
fx (x) = { rOp-e-=/8
%3D
I< 0.
Consider the reciprocal variable, Y = x.
(a) Consider the cumulative distribution function (cdf) of Y, Fy(y). Write Fy (y)
in terms of the cdf of X, Fx.
(b) Verify that the cdf you derived above is a valid cdf.
(c) Consider the probability density function (pdf) of Y, fy(y). Show that the pdf
of Y is,
fy(y) =
y > 0;
y<0.
(d) Verify that the pdf above is a valid pdf.
(e) Find the moments of Y directly by evaluating,
!!
where k is a positive integer.
(f) Show that the moment generating function (mgf) of Y does not exist. That is,
My (t) = E(e") = | c"f(v) dy,
%3D
does not exist.
Transcribed Image Text:Question 3 Let X~ Gamma(a, B) be a Gamma random variable. That is, >0; fx (x) = { rOp-e-=/8 %3D I< 0. Consider the reciprocal variable, Y = x. (a) Consider the cumulative distribution function (cdf) of Y, Fy(y). Write Fy (y) in terms of the cdf of X, Fx. (b) Verify that the cdf you derived above is a valid cdf. (c) Consider the probability density function (pdf) of Y, fy(y). Show that the pdf of Y is, fy(y) = y > 0; y<0. (d) Verify that the pdf above is a valid pdf. (e) Find the moments of Y directly by evaluating, !! where k is a positive integer. (f) Show that the moment generating function (mgf) of Y does not exist. That is, My (t) = E(e") = | c"f(v) dy, %3D does not exist.
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