Question: Let 2 and Y be discrete random variables taking values 0 with the corresponding distributions P(Z-1)= a and P(Y=112) - (1) Find the ML

Let 2 and Y be discrete random variables taking values 0 with the corresponding distributions P(Z-1)= a and P(Y=112) - (1) Find the ML estimator of (a, y) (giving an explicit formula whenever possible) and derive its asymptotic distribution. C12 1+eve (ii) Suppose we want to test Ho: a = y using the asymptotic approach. Derive the t-test statistic and describe in detail how you would perform the test. (iii) Suppose we want to test Ho: a = 1/2. Provide the bootstrap LR (likelihood ratio) test statistic. No need to describe the entire algorithm.

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