Suppose for this problem that true IQ is a meaningful concept rather than a reified
Chapter 9, Problem 46(choose chapter or problem)
Suppose for this problem that true IQ is a meaningful concept rather than a reified social construct. Suppose that in the U.S. population, the distribution of true IQs is Normal with mean 100 and SD 15. A person is chosen at random from this population to take an IQ test. The test is a noisy measure of true ability: its correct on average but has a Normal measurement error with SD 5. Let be the persons true IQ, viewed as a random variable, and let Y be her score on the IQ test. Then we have Y | N (, 52 ) N (100, 152 ). (a) Find the unconditional mean and variance of Y . (b) Find the marginal distribution of Y . One way is via the MGF. (c) Find Cov(,
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