A system for a random amount of time X (in units of months) is given by a density -x/2 xe f(x) = ; x>0, ; x<0. Find the moment generating function of X. Hence, compute the variance of X. (a) (b) Deduce the expression for the k th moment. 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. (c)
A system for a random amount of time X (in units of months) is given by a density -x/2 xe f(x) = ; x>0, ; x<0. Find the moment generating function of X. Hence, compute the variance of X. (a) (b) Deduce the expression for the k th moment. 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. (c)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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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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![A system for a random amount of time X (in units of months) is given by a density
/2
xe
; x>0,
; x<0.
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.
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.
(c)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F60abd4de-ba2d-4a53-b8fc-e1d2e0799cec%2Fd9fa3e72-1098-478a-bfbb-0db58ff147f3%2Fuh2t82_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
/2
xe
; x>0,
; x<0.
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.
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.
(c)
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