image 6.120 Choose the appropriate distribution. You must decide which of two discrete distributions a random variable X has. We will call the distributions p0 and p1. Here are the probabilities they assign to the values x of X:

x 0 1 2 3 4 5 6
p0 0.1 0.1 0.2 0.3 0.1 0.1 0.1
p1 0.1 0.3 0.2 0.1 0.1 0.1 0.1

You have a single observation on X and wish to test

H0: p0 is correct

Ha: p1 is correct

One possible decision procedure is to reject H0 only if X ≤ 1.

  1. (a) Find the probability of a Type I error, that is, the probability that you reject H0 when p0 is the correct distribution.

  2. (b) Find the probability of a Type II error.