2007 Exam 2.1Solutions

# 2007 Exam 2.1Solutions - IE 111 9:00 Section Exam 2 Fall...

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IE 111 NAME ___Solutions_____________ 9:00 Section Exam 2 Fall 2007 Average = 76.4 SD = 11.1 Median = 74.5 N = 27 50's 38 60's 44799 70's 123344566899 80's 344 90's 12466

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Question 1. Suppose a biased coin is flipped 3 times. Let X be the number of heads in 3 flips. The PMF of X is partially shown below: P(X=0) = ? P(X=1) = 12/27 P(X=2) = 6/27 P(X=3) = ? a) Find the values for the question marks above. P(X=1) = 3 C 1 (p) 1 (1-p) 2 = 12/27 = (3) (p) 1 (1-p) 2 4/27 = (p)(1-p) 2 so p=1/3 by inspection (sorry) P(X=0) = (2/3) 3 = 8/27 P(X=3) = (1/3) 3 = 1/27 b) Find the expected value of X X~Binomial (N=3, p=1/3) E(X) = Np = 1 OR (1/27)[ (0)(8) + (1)(12) + (2)(6) + (3)(1) ] = 1 c) What is the probability of a head on a single flip? P = 1/3 from part a)
Question 2. Consider the following Probability Mass Function that you have never seen before: = = - ,.... , 2 , 1 , 0 for ! ) ( x x e x f x X λ a) What is (are) the parameter(s) of this distribution? The parameter is

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2007 Exam 2.1Solutions - IE 111 9:00 Section Exam 2 Fall...

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