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.
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Author:Sheldon Ross
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![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8c977c24-ef01-4548-938c-030883f96222%2Fded3c923-fba0-4d68-8564-7a5818e27d41%2Fmuei62t_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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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