Homework Answers
3.
P(X) = .4
P(Y) = .5
P(XY) = P(X) * P(Y) = .4*.5 = .20
P(X or Y) = P(X) + P(Y) = .4 + .5 = .9
P(Y/X) = P(XY)/P(X) = .2/.4 = .5
4.
P(Y/X) = P(XY)/P(X) = (.4*.3)/.4 = .3
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13. If the events X and Y are independent and P(X) = .4 and P(Y) =...
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5. X and Y are independent with X ~ Binom(mp) and Y ~ Binom(m, p). Make Z = X + Y. What is the conditional distribution of X, given Z?
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81. Consider the function g(x, y) given by, 1 1.52.53 11/4 0 0 0 2 0 1/8 0 0 y 3 0 1/4 0 0 4 0 0 1/4 0 5 00 0 1/8 and complete / determine the following: (a) Show that g(x, y) satisfies the properties of a joint pmf. (See Table in ?6.0.1.) (b) P(X < 2.5,Y < 3) (c) P(X < 2.5) (d) P(Y < 3) (e) P(X> 1.8, Y> 4.7) (f) E[X], EY], Var(X), Var(Y)...
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