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Unformatted text preview: i (i = 0, 1, 2, . ..). Define For all values of t such that h(t) is finite. Find M k h(t) / M t k * t=1 and identify it. 2 (20) 3. Consider two random variables Y 1 and Y 2 with joint p.d.f.: (a) Find the value of c which makes this a p.d.f. (b) Find P(Y 1 # .75, Y 2 $ .50). (20) 4. Consider the random variable X with p.d.f. where " > 0, $ > 0, and B( " , $ ) is the beta function. Find the p.d.f. of Y = 1/(1 + X) and identify it. (20) 5. Consider two random variables X and Y, where X = price and Y = quantity. Researcher A predicts quantity given price with E*(Y|X), making prediction error U = Y -E*(Y|X). Researcher B predicts price given quantity with E*(X|Y), making prediction error V = X - E*(X|Y). Find Cov(U, V) and express it in terms of the correlation D XY between price and quantity....
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- Fall '10