The number of attempts required to successfully transmit a message across a noisy channel can be modeled by a geometric distribution, whose pmf is (1 – p)^x–1p for x = 1, 2, 3, …. To estimate the unknown parameter p we obtain the random sample X₁, X₂, …, X_n from this geometric distribution. 

a. Find the Fisher information in a single observation X using both (7.5) and (7.6).

b. What is the Fisher information in the random sample?

c. Determine the Cramér–Rao lower bound for the variance of an unbiased estimator of p.

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E|-000 - In (f(X; 0)) I(0) = E