Let Y be the rate (calls per hour) at which calls arrive
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Let Y be the rate (calls per hour) at which calls arrive at a switchboard. Let X be the number of calls during a two-hou
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Let Y be the rate (calls per hour) at which calls arrive at a switchboard. Let X be the number of calls during a two-hour period. Suppose that the marginal p.d.f. of Y is f2(y) = e?y if y > 0, 0 otherwise, and that the conditional p.f. of X given Y = y is g1(x|y) = ? ? ? (2y)x x! e?2y if x = 0, 1,..., 0 otherwise. a. Find the marginal p.f. of X. (You may use the formula ? 0 yke?y dy = k!.) b. Find the conditional p.d.f. g2(y|0) of Y given X = 0. c. Find the conditional p.d.f. g2(y|1) of Y given X = 1. d. For what values of y is g2(y|1)>g2(y|0)? Does this agree with the intuition that the more calls you see, the higher you should think the rate is?
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