(c)and the moment generating function of Y.Define the random variable Y = X1+X2+.+Xp. Find E(Y), Var(Y)(d)Consider a random variable X having Gamma(a, X) distribution,{, x > 0, otherwisefx(x) =T(a)Show that the moment generating function of the random variable X is mx(s)X°a-r for s< A, where I'(a) is%3DI(a) = | .pa-le-# dx.(e)What is the probability distribution of Y given in (c)? Explain youranswer. Let X1, X2, ..., Xn be a sequence of independent and identically distributedrandom variables having the Exponential(A) distribution, A > 0,de-dr,r >0fx,(x) = { 0, otherwise(a)s< A;Show that the moment generating function mx(s) := E(e®X) = , for(b)Using (a) find the expected value E(X;) and the variance Var(X;).

Let X1, X2, ..., Xn be a sequence of independent and identically distributed random variables having the Exponential(X) distribution, A> 0, fx, (2) = { ( de-Ar , r>0 , otherwise Show that the moment generating function mx(s) := E(e*X) = for (a) s< A; (b) Using (a) find the expected value E(X;) and the variance Var(X;).

Let X1, X2, ..., Xn be a sequence of independent and identically distributed random variables having the Exponential(X) distribution, A> 0, fx, (2) = { ( de-Ar , r>0 , otherwise Show that the moment generating function mx(s) := E(e*X) = for (a) s< A; (b) Using (a) find the expected value E(X;) and the variance Var(X;).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section: Chapter Questions

Problem 9T

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Question

(c)
and the moment generating function of Y.
Define the random variable Y = X1+X2+.+Xp. Find E(Y), Var(Y)
(d)
Consider a random variable X having Gamma(a, X) distribution,
{
, x > 0
, otherwise
fx(x) =
T(a)
Show that the moment generating function of the random variable X is mx(s)
X°a-r for s< A, where I'(a) is
%3D
I(a) = | .
pa-le-# dx.
(e)
What is the probability distribution of Y given in (c)? Explain your
answer.

Let X1, X2, ..., Xn be a sequence of independent and identically distributed
random variables having the Exponential(A) distribution, A > 0,
de-dr
,r >0
fx,(x) = { 0
, otherwise
(a)
s< A;
Show that the moment generating function mx(s) := E(e®X) = , for
(b)
Using (a) find the expected value E(X;) and the variance Var(X;).

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