UCLA Statistics Probability Questions
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For a freshman taking introductory statistics andmajoring in psychology, let X equal the students ACTmathematics score and Y the students ACT verbal score.Assume that X and Y have a bivariate normal distribu-tion with ?X = 22.7, ?X2 = 17.64, ?Y = 22.7, ?Y2 = 12.25,and ? = 0.78.
(a) Find P(18.5 < Y < 25.5).(b) Find E(Y | x).
(c) FindVar(Y|x).
(d) Find P(18.5 < Y < 25.5|X = 23).(e) Find P(18.5 < Y < 25.5|X = 25).
(f) For x = 21,23, and 25, draw a graph of z = h(y|x)similar to Figure 4.5-1.
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