Let Y1 and Y2 be independent and identically distributed with a uniform distribution over the interval (, + 1). For testing H0 : = 0 versus Ha : > 0, we have two competing tests: Test 1: Reject H0 if Y1 > .95. Test 2: Reject H0 if Y1 + Y2 > c. Find the value of c so that test 2 has the same value for as test 1. [Hint: In Example 6.3, we derived the density and distribution function of the sum of two independent random variables that are uniformly distributed on the interval (0, 1).]

Lecture 7: 8.5 General Continuous Random Variables Definition: - A curve (or function) is called a Probability Density Curve if: 1. It lies on or above the horizontal axis. 2. Total area under the curve is equal to 1. - KEY IDEA: AREA under a density curve over a range of values corresponds to the PROBABILITY...