[Solution Library] Consider a random sample of size n from a Poisson distribution, Xi ~ POI (mu). Find the CRLB for the variances of unbiased estimators
Question: Consider a random sample of size n from a Poisson distribution, Xi ~ POI (mu).
- Find the CRLB for the variances of unbiased estimators of mu.
- Find the CRLB for the variances of unbiased estimators of theta = e^-mu.
- Find a UMVUE of mu.
- Find the MLE theta hat of theta.
- Is theta hat an unbiased estimator of theta?
- Is theta hat asymptotically unbiased?
- Show that theta tilde = [(n-1)/n]^(sum of Xi) is an unbiased estimator of theta.
- Find Var (theta tilde) and compare to the CRLB of (b).
Hint: Note that Y = Sum of Xi ~ POI (n mu), and that E (theta tilde) and Var (theta tilde) are related to the MGF of Y.
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