Consider a biased coin where the probability of a head p is

Consider a biased coin, where the probability of a head, p, is know to be 0.2, 0.3, or 0.8. The coin is tossed repeatedly, and we let x be the number of tosses required t obtain the first head. To test H0: p=0.8, suppose we reject H0 if X>3, and do not reject otherwise. 1) what is the probability of type 1 error.

2) what is the probability of a type 2 error for each of the other two values of p?

3) For a test of H0:p=0.3, suppose we use a critical region of the form {1,1,15...}. Find type 1 and type 2 errro for each of the other values of p.

Solution