3. The lifetime of a certain computer chip that your company manufactures is characterized by the population distribution fðz; yÞ ¼ 1 y ez=y Ið0;1Þ ðzÞ;

where z is measured in thousands of hours. Let (X1, ..., Xn)

represent iid random variables with the density f(z;y) . An outcome of the random variableYn ¼ 1 þ Pn i¼1 Xi

=nwill to be used to provide an estimate of y.

(a) Is it true that Yn!

m y? Is it true that Yn!

p y?

(b) Define an asymptotic distribution for Yn.

(c) Suppose n ¼ 100 and y ¼ 10. Use the asymptotic distribution you defined in

(b) to approximate the probability that Yn  15.