Stat 321 – HW 8

Due Tuesday, March 11

1) Suppose X₁, X₂, X₃ denotes a random sample from the exponential distribution. Consider the following four estimators of q:

(a) Which of the above estimators are unbiased for ?

(b) Among the unbiased estimators of , which has the smallest variance?

2) Exercise #13 (p. 242)

3) Exercise #18 (p. 243)

4) Exercise #22 (p. 251) part(a) only

5) The reading on a voltage meter connected to a test circuit is uniformly distributed over the interval (q, q+1), where q is the true but unknown voltage of the circuit. Suppose X₁,…,X_n denotes a random sample of readings from this voltage meter.

(a) Show that is a biased estimator of q. Hint: What is E(X)? E()?

(b) Find a function of that is an unbiased estimator of q.

(c) Determine the method of moments estimator of q.

(d) Determine the variance of the method of moments estimator you found in (c). Hint: What is V(X)? V()?