Midterm2

# Midterm2 - Math 311 Probability and Statistics I Midterm#2...

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Math 311. Probability and Statistics I Midterm #2 Your name: Reminder: Explain your answers. e = lim x →∞ (1 + 1 /x ) x = 2 . 7182818 ... ( n k ) = n ( n - 1) ··· ( n - k +1) k ( k - 1) ··· 1 1

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1. (15pts) In order to pass a test you need to get at least 3 out of 5 problems cor- rect . Assume that the probability you get each problem wrong is 0.2. What is the probability that you pass the test ? (10pts) In another test you have 10 extremely diﬃcult problems to solve. Assume that the probability that you get each problem solved is 0.1. Using a Poisson ap- proximation, what is the approximate probability that you solve at most 1 problem ? (Without using Poisson approximation, the answer is: 2 x =0 ( 10 x ) (0 . 1) x (0 . 9) 10 - x = 0 . 7360989291. So you have a ground for comparison.) 2
2. Let X be a hypergeometric r.v. with parameters N = 100, M = 40, n = 3. (5pts) Work out the p.m.f. of X . Please calculate the numerical values of all proba- bilities. (5pts) Let

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Midterm2 - Math 311 Probability and Statistics I Midterm#2...

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