3. The lifetime of a certain computer chip that your company manufactures is characterized by the population distribution

"II z,. B) -_ (1j e -z/B 110,00) (z) , where z is measured in thousands of hours. Let

(X I, ... , Xn) represent iid random variables with the density f(z; B). An outcome of the random variable Yn :=

(1 + 2::7=1 Xd/n will be used to provide an estimate of e.

a. Is it true that Yn ..E4 ()? Is it true that Yll --4 ()?

b. Define an asymptotic distribution for Yll •

c. Suppose n = 100 and B := 10. Use the asymptotic distribution you defined in

(b) to approximate the probability that Yll ~ 15.