61. The principle of unbiasedness (prefer an unbiased estimator to any other) has been criticized on the grounds that in some situations the only unbiased estimator is patently ridiculous. Here is one such example. Suppose that the number of major defects X on a randomly selected vehicle has a Poisson distribution with parameter l. You are going to purchase two such vehicles and wish to estimate u 

P(X1  0, X2  0)  e2l, the probability that neither of these vehicles has any major defects. Your estimate is based on observing the value of X for a single vehicle. Denote this estimator by .

Write the equation implied by the condition of unbiasedness, E[d(X)]  e2l, cancel el from both sides, then expand what remains on the right-hand side in an in nite series, and compare the two sides to determine d(X). If X  200, what is the estimate?

Does this seem reasonable? What is the estimate if X  199? Is this reasonable?