Reminder: Please do not take from other answersPlease type the answers A system for a random amount of time X (in units of months) is given by a densityf(x) =xe2 ; r>0,: x<0.(a)Find the moment generating function of X. Hence, compute the variance ofX.(b)Deduce the expression for the k th moment.(c)Obtain the distribution function of X. Hence, compute that the probabilitythat, 7 of such system, at least 4 will function for at least 6 units of months.State the assumptions that you make.

The moment generating function is defined as MX(t)=EetX

A system for a random amount of time X (in units of months) is given by a density (txe2 : x>0, : xs0. f(x)=. Find the moment generating function of X. Hence, compute the variance of X. (a) (b) Deduce the expression for the k th moment.

A system for a random amount of time X (in units of months) is given by a density (txe2 : x>0, : xs0. f(x)=. Find the moment generating function of X. Hence, compute the variance of X. (a) (b) Deduce the expression for the k th moment.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Please type the answers

A system for a random amount of time X (in units of months) is given by a density
f(x) =xe2 ; r>0,
: x<0.
(a)
Find the moment generating function of X. Hence, compute the variance of
X.
(b)
Deduce the expression for the k th moment.
(c)
Obtain the distribution function of X. Hence, compute that the probability
that, 7 of such system, at least 4 will function for at least 6 units of months.
State the assumptions that you make.

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