Question: Consider a random sample X1; : : : ;Xn from a population X with support on non-negative integers. A simple null hypothesis H0 assumes that

Consider a random sample X1; : : : ;Xn from a population X with support

on non-negative integers. A simple null hypothesis H0 assumes

that X has a Poisson distribution with mean 1. A simple alternative

hypothesis H1 assumes that X has a geometric distribution with mean

2.

a. Find a best critical region for testing H0 against H1.

b. Let n = 1 and the best critical region C = f0; 3; 4; : : :g. Compute the

level of significance and power.

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