The principle of unbiased estimation has been criticized on the grounds that in some situations the of fruit has a Poisson distribution with parameter μ. You are going to purchase two such pieces of fruit and wish to estimate

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0=e-2", the probability that neither of these has any blemishes. But your estimate is based on observing the value of X for a single piece. Obtain an estimator 0 = d(X) that is unbiased for 0; i.e., such that E[d(X)]=e-2". Set the summation for E[d(X)] equal to e-2", cancel e¯" from both sides, then expand what remains on the right-hand side in a Taylor 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? =