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2. In a given population, weight [Y] and height [X] have a joint distribution with mean 1.1:: = 170, cry: 28, [.lx= 66, 0x: 3 and cov[X,Y) = 45,

2. In a given population, weight [Y] and height [X] have a joint distribution with mean 1.1:: =
170, cry: 28, [.lx= 66, 0x: 3 and cov[X,Y) = 45, where Yis measured in pounds and X is
measured in inches. Suppose that the regression function for Ygiven X is linear: E(Y|X] 2 ﬁg + ﬁx [a] What are the values of ﬁg and {31? (b) Let u = Y — (ﬂ; + 61);]. What is the mean, variance and standard deviation of u? [c] A person is selected at random from the population and X = 68. What is your prediction
fo the person's weight? Suppose the regression function for height given weight is linear: E(X|l’) = go + ﬁl’.
(d) What are the values of )0 and 71? (e) Let v = X —— [70 + 91X). What is the mean, variance and standard deviation of v? (f) A person is selected at random from the population and Y: 180. What is your
prediction for the person's height?

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