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Example 7.2.1: Let X1,...Xn be iid(k,p) binomial... step by step show how k and p were obtained (show all algebra steps) thank you
Example 7.2.2: Let Xi,.. Xn be iid binomial(k, p), that is, Here we assume that both k and p are unknown and we desire point estimators odel has for both parameters. (This somewhat unusual application of the binomial m been used to estimate crime rates for crimes that are known to have many unre occurrences. For such a crime, both the true crime rate, p, and the total numberof occurrences, k, are unknown.) ported Equating the first two sample moments to those of the population yields the system of equations P, 7l
e) SECTION 72 Methods of Finding Estimators 287 which now must be solved for k and p. After a little algebra, we obtain the method of moments estimators and p=頁. Admittedly, these are not the best estimators for the population parameters. In particular, it is possible to get negative estimates of k and p which, of course, must bie e numbers. (This is a case where the range of the estimator does not coincide positiv with the range of the parameter it is estimating.) However, in fairness to the me of m smaller than the sample variance thod oments, note that negative estimates will occur only when the sample mean is , indicating a large de gree of variability in the data
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