I will flip a coin three times and let X stand for the number of times that the coin comes up heads. Let θ stand for the probability that the coin comes up heads on a single flip, and assume that the flips are independent given θ. I wish to test the null hypothesis H0 : θ = 1/2 against the alternative hypothesis H1 : θ = 3/4. Find the test δ that minimizes α(δ) + β(δ), the sum of the type I and type II error probabilities, and find the two error probabilities for the test.