For a certain class of jet engines the time until an

Reference no: EM13609108

For a certain class of jet engines, the time until an overhaul is needed, Y (measured in years), varies according to the following probability density function: cye^-y/2, y > 0 fY (y) = 0, otherwise.

(a) What is the value of c? Hint: Is this a special gamma density?

(b) Find E(Y ) and var(Y ).

(c) Find the probability that an engine's time to overhaul is less than one year. Would you consider this event unusual? Why or why not?

(d) What is the probability that the time to overhaul is longer than 4 years? Would you consider this event unusual? Why or why not?

e) Let t be a fixed constant. Show that, for t<1/2,

E(e^(tY))= Integral from 0 to infinity of e^(ty)fY(y)dy= [1/(1-2t)]^2

Reference no: EM13609108

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