MATH 302 Midterm: MATH 302 2015 Winter Test 1
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Notes or other electronic devices are not allowed: the last page is empty for additional space. If a question is solved there, mark it clearly or it may not be graded. N ( , 2) p(1 p)k 1 (cid:0)n k(cid:1)pk(1 p)n k (cid:0)n+k 1 n 1 (cid:1)pn(1 p)k e k k! The probability that p(0 < z < x), where z n (0, 1): x. Assume that x, y are independent random variables such that e(x) = 1, var(x) = 2, E(y ) = 3, and var(y ) = 4. (a) calculate e(2x + 4xy y ). Let x, y be independent exponential random variables with the same parameter . Find the probability density function of x y . A random variable x has moment generating function gx(t) = (1 3t) 2 for t < 1/3. (a) find e(x). Assume that the random variables x, y have joint density function f (x, y) =(c(3x2 + 2y)
