MA 421 Test II

MA 421 Test II - MA 421 Exam II(Total = 100 points Show all...

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MA 421 Exam II 11/2/07 (Total = 100 points) Show all work!! 1. The distribution function of a random variable X is given by F ( x )= 0 x< - 1 ( x +1) 2 4 - 1 0 1 2 0 1 1 8 x + 3 4 1 2 12 x. a) (20 pts.) Find P ( X = i ), i = - 1 , 0 , 1 , 2. b) (5 pts.) Find P (0 X< 3 2 ). 2. (25 pts) Let S = { s 1 ,s 2 3 4 } with P ( { s 1 } P ( { s 2 } )=1 / 8, P ( { s 3 } 1 / 2, and P ( { s 4 } / 4. Let X : S -→ R be the random variable defined as: X ( s 1 X ( s 3 - 2, X ( s 2 ) = 1, and X ( s 4 ) = 2. Find the probability mass function of X , E ( X ) , and Var( X ). 3. (5 pts) Let X be a binomially distributed random variable with parameters n =4 , p =1 / 3. Then P ( X 2)=(pick one): a) 16/27; b) 11/27; c) 16/81; d) 32/81. 4. (10 pts.) If 3% of the school children in a large city have I.Q.’s over 150, use Poisson approximation to determine the probability that out of 60 of the children randomly selected, exactly 2 will have I.Q.’s over 150.
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