Solved: Do the same task as in Frob. 13 if the given
Chapter 25, Problem 25.1.14(choose chapter or problem)
Consider X = Number of independent trials until an event A occurs. Show that X has the probability function \(f(x)=p q^{x-1}, x=1,2, \cdots\), where p is the probability of A in a single trial and q = 1 - p. Find the maximum likelihood estimate of p corresponding to a sample \(x_{1}, \cdots, x_{n}\) of observed values of X.
Text Transcription:
f(x) = pq^{x - 1}, x = 1, 2, cdots
x_1, cdots, x_n
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