Math511Exam2Solutions

6 12 2 npq 12 04 48 b p x 9

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Unformatted text preview: d is followed by a blue card. Let X denote the number of cards drawn. Examples: BBBRRB 6- draws, RB 2- draws, RRRB 4- draws, BRRRRRB 7- draws. E(X) = 4.5 (Reduce to a decimal) Solution: Let X R = # draws needed to get a Red card, and X B = # draws needed to get a Blue card. 1 Then X = X R + X B , and so E ( X ) = E ( X R ) + E ( X B ) = 1 1 + = 3 + 1.5 = 4.5 2 3 3 (b). Suppose that X is a Poisson random variable and P ( X = 1) = P ( X = 2 ) . Determine the value of P( X = 3) = (Exact in terms of e) λ 2e− λ Solution: From P ( X = 1) = P ( X = 2 ) , we get that λ e −...
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