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).

Metabolism, Energy Balance and Weight Control: Part 1 --- October 27 Why is a healthy weight important For overall health and to prevent and maintain diseases and conditions Overweight or Obesity o Overweight: having extra body weight from muscle, bone, fat, and water o Obesity: having a high amount of extra fat 34% of...