Let x1, ... , x4 be a random sample from a Geometric(p) distribution. Suppose we observed (x1, x2, x3, x4) = (2, 3, 3, 5). Find the likelihood function using Px_i(xi; p) = p(1 - p)^{xi-1} as the PMF.
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The likelihood function is the product of the probability mass functions (PMFs) for each observation in the sample. The PMF for a Geometric(p) distribution is given by P(x; p) = p(1-p)^{x-1}. Now, we can plug in the observed values (x1, x2, x3, x4) = (2, 3, 3, Show more…
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