Question: Let X have a negative binomial distribution with parameters r and p. Find the most powerful test of H0 : r = 2,p = 1/2

Let X have a negative binomial distribution with parameters r and p. Find the most powerful test of H0 : r = 2,p = 1/2 against H1 : r = 4,p = 1/2 at significance level α = 0.05. Find probability of type II error. Use randomized test if necessary.

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