A system for a random amount of time X (in units of months) is given by a density Stxe¯² ; x>0, f(x)=< ; x<0. Find the moment generating function of X . Hence, compute the variance of Х. 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.

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A system for a random amount of time X (in units of months) is given by a density
-x/2
; х>0,
f (x)=tew:
x<0.
Find the moment generating function of X . Hence, compute the variance of
X .
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.
Transcribed Image Text:A system for a random amount of time X (in units of months) is given by a density -x/2 ; х>0, f (x)=tew: x<0. Find the moment generating function of X . Hence, compute the variance of X . 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.
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