# hw03 - / 10 P [ A 3 | A c 1 A c 2 ] = 1 / 10 Express all...

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ENEE 324 ASSIGNMENT 3 Due Tue 09/15 Problem 3.1 The outcome of a random experiment is a pair of integers ( i,j ) in { 1 , 9 } 2 . The probability mass function for the eighty-one outcomes is depicted below, where each symbol represents a diﬀerent probability value: = r , / = 2 r , 4 = 3 r , = 4 r and * = 5 r * 1 i 9 9 j 1 Express all answers below as ratios of integers. (i) (5 pts.) Determine the value of r . (ii) (5 pts.) Determine the probability of the event A = { ( i,j ) : i = j } . (iii) (5 pts.) Using your answer to part (ii) and a symmetry argument, determine the probability of the event B = { ( i,j ) : j > i } . (iv) (5 pts.) Determine the conditional probability P [ D | B ], where D = { ( i,j ) : i > 4 } . Problem 3.2 Events A 1 , A 2 and A 3 are such that: P [ A 1 ] = 3 / 10 P [ A 2 | A 1 ] = 6 / 10 P [ A 2 | A c 1 ] = 8 / 10 P [ A 3 | A 1 A 2 ] = 5 / 10 P [ A 3 | A c 1 A 2 ] = 2 / 10 P [ A 3 | A 1 A c 2 ] = 7
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Unformatted text preview: / 10 P [ A 3 | A c 1 A c 2 ] = 1 / 10 Express all answers below as ratios of integers. (i) (8 pts.) Determine the probabilities of the eight events B 1 B 2 B 3 , where B i = A i or B i = A c i , and mark them on the appropriate Venn diagram. (ii) (2 pts.) Determine P [ A 3 ]. (iii) (3 pts.) What is the probability that exactly one of the events A 1 , A 2 and A 3 occurs? (iv) (3 pts.) What is the probability that two or more of the events A 1 , A 2 and A 3 occur? (v) (4 pts.) What is the conditional probability that all of the events A 1 , A 2 and A 3 occur, given that two or more of them have occurred?...
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## This note was uploaded on 03/21/2010 for the course ENEE 324 taught by Professor Ephrimedes during the Fall '05 term at Maryland.

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