Refer to Exercise 3.86. The maximum likelihood estimator for p is 1/Y (note that Y is the geometric random variable, not a particular value c of it). Derive E(1/Y ). [Hint: If | | < 1,   

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Consider an extension of the situation discussed in Example 3.13. If we observe y₀ as the value for a geometric random variable Y , show that P(Y = y₀) is maximized when p = 1/y₀. Again, we are determining (in general this time) the value of p that maximizes the probability of the value of Y that we actually observed.

  

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Suppose that we interview successive individuals working for the large company discussed in Example 3.10 and stop interviewing when we find the first person who likes the policy. If the fifth person interviewed is the first one who favors the new policy, find an estimate for p, the true but unknown proportion of employees who favor the new policy.

  

     

Er'li = - In(1 r).] i3D