Can't figure these out, please help.
4. Suppose X and Y be independent normal random variables, with distributions N(μ, sigm) = N(5, 3) and N(2, 4) respectively. Let W = X + 2Y + 1.
Compute
(a) E(W); (b) V (W); (c) Prob(W < 0) (d) Cov(X,W) .
5. Suppose that X and Y are rv’s which only assume the values 0 and 1. Suppose that the joint pmf p(x, y) satisfies p(0, 0) = .3, p(0, 1) = .4, p(1, 0) = .2.
(a) What is p(1, 1)?
(b) Compute E(2X − Y ).
(c) Are X and Y independent?
(d) Compute the conditional pmf pX(x).
6. Suppose that the number of phone calls Tara receives in the evening is a Poisson process with rate 2 per hour, and the number of calls I receive is an independent Poisson process with rate 0.1 per hour.
(a) At 6 p.m., Tara returns home and happily waits for her next
phone call. What is the probability that she will get a call before 7:30 pm?
(b) What is the probability that at least one of us receives at least one phone call between 6 and 7:30 pm?
2007-08-13
16:25:37
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2 answers
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asked by
Anonymous