Unformatted text preview: H s? What is the probability that exactly four H s are obtained? (ii) (6 pts.) Suppose that the number N of homework problems assigned during a semester is a random variable with geometric pmf P [ N = n ] = 2n , n ≥ 1 Given N = n , the total time T (e.g., in hours) spent on homework has conditional pdf f ( t ) = 3 n t n1 ( n1)! · e3 t , t ≥ Determine E [ T  N = n ] (a known integral, already encountered in this class) and hence E [ T ]. (iii) (7 pts.) Let X be Gaussian with E [ X ] =2 and Var[ X ] = 9. Let the conditional distribution of Y given X = x also be Gaussian with mean E [ Y  X = x ] =2 x + 1 and variance E [ Y 2  X = x ]( E [ Y  X = x ]) 2 = 4 Determine E [ Y ], Var[ Y ] and E [ XY ]....
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 Fall '05
 Ephrimedes
 Probability theory, pts

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