winter 2007 STAT 230 test-2-soln-07W

# winter 2007 STAT 230 test-2-soln-07W - STAT 230 Name Test 2...

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STAT 230 Test 2 January 31, 2007 3:30 pm – 4:10 pm Name: ID#: UWUserid: Circle Your Section Number : 001 (10:30) 002 (12:30) 003 (1:30) 004 (2:30) 1. Suppose Johnny gives you a loaded die and tells you that the probability of obtaining a particular number is proportional to that number squared. That is, if X is the number you obtain after tossing the die, then P ( X = x ) = cx 2 , x = 1 , ..., 6 for some constant c . [4] (a) Find the appropriate value of c and tabulate the probability function of X , f ( x ). f ( x ) = x 2 91 , x = 1 , 2 , 3 , 4 , 5 , 6 . [4] (b) Find P ( X < 3). P ( X < 3) = f (1) + f (2) = 1 91 + 4 91 = 5 91 . [4] (c) Find P ( X = 1 | X < 3). P ( X < 3) = P ( X = 1 and X < 3) P ( X < 3) = P ( X = 1) P ( X < 3) = 1 / 91 5 / 91 = 1 5 .

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2. A deck of 52 cards contains 26 red cards and 26 black cards. Johnny ﬁrst tosses a (fair) die (with six faces: 1, 2, 3, 4, 5, 6). If he obtains an even number, he will draw 2 cards from the deck without replacement . If he obtains an odd number, he will draw 2 cards from the deck
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winter 2007 STAT 230 test-2-soln-07W - STAT 230 Name Test 2...

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