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For a female freshman in a health fitness program, let X equal her percentage of body
Chapter 4, Problem 4.5-11(choose chapter or problem)
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 X = 24.5, 2 X = 4.82 = 23.04, Y = 0.2, 2 Y = 3.02 = 9.0, and = 0.32. Find (a) P(1.3 Y 5.8). (b) Y|x, the conditional mean of Y, given that X = x. (c) 2 Y|x, the conditional variance of Y, given that X = x. (d) P(1.3 Y 5.8 | X = 18).
Questions & Answers
QUESTION:
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 X = 24.5, 2 X = 4.82 = 23.04, Y = 0.2, 2 Y = 3.02 = 9.0, and = 0.32. Find (a) P(1.3 Y 5.8). (b) Y|x, the conditional mean of Y, given that X = x. (c) 2 Y|x, the conditional variance of Y, given that X = x. (d) P(1.3 Y 5.8 | X = 18).
ANSWER:Step 1 of 5
Given:
The variable X represents the female percentage of body fat at the beginning of the program.
The variable Y represents the change in her percentage of body fat measured at the end of the program.
The variables X and Y have a bivariate normaldistribution.
The values are given as,
