b) The random variable X, has probahility density function(nents1>0fa(2) =otherwiseUsing the moment generating functions, show that(i) X, has a limiting distribution which is degenerate at x = 8(ii) Z, = n(X, - 8) has a limiting distribution which is exponential with mean 1.%3!

We have fx=ne-nx-θ x>00 otherwise

bị The random variahle X, has probahility density function 1>0 otherwise L'sing the moment generating functions, show that X, has a limiting distribution which is degenerate at z = 6 ) Z. = n(X, - 0) has a limiting distribution which is exponential with mean 1.

bị The random variahle X, has probahility density function 1>0 otherwise L'sing the moment generating functions, show that X, has a limiting distribution which is degenerate at z = 6 ) Z. = n(X, - 0) has a limiting distribution which is exponential with mean 1.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

b) The random variable X, has probahility density function
(nents
1>0
fa(2) =
otherwise
Using the moment generating functions, show that
(i) X, has a limiting distribution which is degenerate at x = 8
(ii) Z, = n(X, - 8) has a limiting distribution which is exponential with mean 1.
%3!

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