Tutorial 8s.pdf - 1(a)N~Geometric(9/19(b E(N)=19/19...

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1. (a)N~Geometric(9/19) (b) E(N)=19/19 Var(N)=(1-9/19)/(9/19)^2 (c) Amount of money lost by n games=1+2+2^2+2^3+ +2^(n-1)=(2^n)-1 Since 1023=(2^10)-1 he can afford up to 10 losing games. (d) If he loses 10 games before winning once, he will lose all his money, i.e. . X=-1023 If he wins once at n th game (n<=10) before he loses all his money, he can win (2^n)-((2^n)-1)=1 dollar, i.e. . X=1 Hence there are only two possible values for X . The pmf of X is given by P(X=-1023)=(10/19)^10=0.0016 P(X=1)=1-(10/19)^10=0.9984. (e) E(X)=1X(1-(10/19)^10)+(-1023)X((10/19)^10=-0.6702 E(X^2)=(1^2)X(1-(10/19)^10))+(1023^2)X(10/19)^10=1707.9266
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