Quiz_2_Solutions - STAT 231 ON-LINE QUIZ 2 SPRING 2010...

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STAT 231 ON-LINE QUIZ 2 SPRING 2010 Solutions Suppose X is a discrete random variable with probability function ( ) (1/ 3) , 0,1,2,. .. x px k x == 1. The value of is (to two decimals) k Since the probabilities add to 1, we have 2 1 1 (1 1/3 (1/3) ...) 11 / 3 kk =+ + += or 2/3 0.67 k 2. is (to three decimals) (5 PX ) + ) 56 52 5 ( 5) 2 / 3 [(1/ 3) (1/ 3) ...] (2 / 3)(1/ 3) [1 1/ 3 (1/ 3) ...] (1 / 3) ≥= × + + + = 3. (to two decimals) ( PXi sodd 35 2 ( ) ( 1) ( 3) . .. (2 / 3)[(1/ 3) (1/ 3) (1/ 3) ...] 1 (2/3)(1/ 3) 1( 1 / 3 ) 1/4 + + = = + Suppose and are independent random variables each with probability function 1 Y 2 Y y 1 2 3 4 () PY y = 1/10 2/10 3/10 4/10 4. If , find (to two decimals) 12 max( , ) WY = Y ) (3 PW = 1 2 1 2 ( 3) ( 1, ( 2, ( 3, ,1 )(3 , 2 ) ( 1 )( 3 ) . . .( 3 2 ) 1323333132 10 10 10 10 10 10 10 10 10 10 27 100 PY Y Y Y Y Y = =+ = +== ×= + =×+×+×+×+× = 5. Find (to two decimals) [] E W
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As above we get 1 (1 ) 100 PW == and 8 (2 ) 100 so by subtraction and hence ( 4) 1 .27 .08 .01 0.64 = = −−−= [ ] 1 0.01 2 0.08 3 0.27 4 0.64 3.54 EW = Assume customers arrive independently at a gas station at a rate of 6 per hour. Let Y be the number of customers who arrive in 8 hours.
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This note was uploaded on 03/20/2011 for the course STATISTICS 231 taught by Professor Mckay during the Spring '10 term at Waterloo.

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Quiz_2_Solutions - STAT 231 ON-LINE QUIZ 2 SPRING 2010...

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