For a female freshman in a health fitness program, let X
Chapter 4, Problem 11E(choose chapter or problem)
PROBLEM 11E
For a female freshman in a health fitness program, let X equal her percentage of body fat at the beginning of the program and Y equal the change in her percentage of body fat measured at the end of the program. Assume that X and Y have a bivariate normal distribution with μX = 24.5, σ2X= 4.82 = 23.04, μY = −0.2,σ2Y = 3.02 = 9.0, and ρ = −0.32. Find
(a) P(1.3 ≤ Y ≤ 5.8).
(b) μ Y|x, the conditional mean of Y, given that X = x.
(c) σ 2 Y|x, the conditional variance of Y, given that X = x.
(d) P(1.3 ≤ Y ≤ 5.8 |X = 18).
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