A memory chip has a projected lifetime X in days. The PDF of the lifetime can be

Question

A memory chip has a projected lifetime X in days. The PDF of the lifetime can be modeled as

fX(x) =

                ke^-x/1000         x > 0

                0                              x < 0

Find the constant k.

Find the probability that the chip will fail within one year.

Find the probability that the chip will fail sometime during its fourth year.

Find cumulative distribution function.

Find the mean time to failure.

Find the mean square of the lifetime.

Find the variance of the lifetime.

Explanation / Answer

a) here as above is a exponential distribution k=1/1000

b) P(X<365) =1-e-x/1000 =1-e-365/1000 =0.3058

c)  probability that the chip will fail sometime during its fourth year =P(3*365<X<4*365)

=(1-e-4*365/1000 )-(1-e-3*365/1000) =0.1023

d)

cumulative distribution function F(x) =1-e-x/1000

e) mean time to failre =1/k =1000

f) mean square of the lifetime E(X2) =2*(E(X))2 =2*10002 =2*106

g)variance =(E(X))2 =10002 =106

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