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Unformatted text preview: ENGM2032, Applied Probability and Statistics Winter 2010 Assignment #4: Solutions 1) a) We use the counting principles of Chapter 2 to determine the probability mass function (pmf) of X . That is, we think of the deck of cards as being composed of two groups, the 13 spades and the 39 other cards. Thus the event X = i means that we have selected i cards from the 13 spades and 4 i cards from the 39 other cards. The desired probabilities are P X = 0 = 13 39 4 52 4 = 39 38 37 36 4 3 2 1 52 51 50 49 4 3 2 1 = 82 , 251 270 , 725 = 0 . 30382 P X = 1 = 13 1 39 3 52 4 = 0 . 43885 P X = 2 = 13 2 39 2 52 4 = 0 . 21349 P X = 3 = 13 3 39 1 52 4 = 0 . 04120 P X = 4 = 13 4 39 52 4 = 0 . 00264 As a check on our math, we note that 0 . 30382+0 . 43885+0 . 21349+0 . 04120+0 . 00264 = 1, as it should. b) To get the expected value of X , we compute E X = 4 X x =0 x P X = x = 0(0 . 30382)+1(0 . 43885)+2(0 . 21349)+3(0 . 04120)+4(0 . 00264) = 1 which makes sense because 1 / 4 of the cards are spades, so one would expect one spade every 4 cards, on average....
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This note was uploaded on 02/24/2010 for the course ENGM 2032 taught by Professor Yao during the Spring '10 term at Dalhousie.
 Spring '10
 yao

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