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A random variable X with two-sided exponential distribution given by has moment generating function given by M X (t)= e^ t +e^ -t -2 t^ 2 .   f x (x)= x+1,&-1\\ 1-x,&0<= x<=1 - 1 <= x <= 0   (a) Using M_{X}(t) or otherwise, find the mean and variance of X.   (b) Use Chebychev inequality to estimate the tail probability, P(X > delta) , for delta > 0 and compare your result with the exact tail probability.

A random variable X with two-sided exponential distribution given by has moment generating function given by M X (t)= e^ t +e^ -t -2 t^ 2 .   f x (x)= x+1,&-1\\ 1-x,&0<= x<=1 - 1 <= x <= 0   (a) Using M_{X}(t) or otherwise, find the mean and variance of X.   (b) Use Chebychev inequality to estimate the tail probability, P(X > delta) , for delta > 0 and compare your result with the exact tail probability.

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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A random variable X with two-sided exponential distribution given by has moment generating function given by M X (t)= e^ t +e^ -t -2 t^ 2 .

 

f x (x)= x+1,&-1\\ 1-x,&0<= x<=1 - 1 <= x <= 0

 

(a) Using M_{X}(t) or otherwise, find the mean and variance of X.

 

(b) Use Chebychev inequality to estimate the tail probability, P(X > delta) , for delta > 0 and compare your result with the exact tail probability.

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