Chapter 6 Discrete Distributions

Chapter 6 Discrete Distributions - Click to edit Master...

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Unformatted text preview: Click to edit Master subtitle style Professor Thomas R. Professor Thomas R. 11 Discrete Distributions Professor Thomas R. Sexton College of Business Stony Brook University Professor Thomas R. Professor Thomas R. 22 Applications in Business o An insurance company needs to set rates for young drivers o A store owner needs to decide how many I- Pods of each model to stock o An airline needs to decide how many seats to overbook on a flight from LaGuardia to OHare. o An investor needs to decide whether to Professor Thomas R. Professor Thomas R. 33 Simple Game: Doubles and Halves o You pay me $5 for the right to play. o You roll a fair die once. o If the number is odd, then I pay you twice the number. o If the number is even, then I pay you half the number. o Is the game fair to you and me? Professor Thomas R. Professor Thomas R. 44 Lets List Your Payoffs Die X =Payoff Probability 1 $2 1/6=0.166667 2 $1 1/6=0.166667 3 $6 1/6=0.166667 4 $2 1/6=0.166667 5 $10 1/6=0.166667 6 $3 1/6=0.166667 Professor Thomas R. Professor Thomas R. 55 Probability Distribution of Payoff Die X =Payoff Probability Cumulative 2 $1 1/6=0.16667 1/6=0.16667 1, 4 $2 1/3 =0.3333 1/2 =0.5 6 $3 1/6=0.16667 2/3=0.66667 3 $6 1/6=0.16667 5/6=0.83333 5 $10 1/6=0.16667 1 Professor Thomas R. Professor Thomas R. 66 Some Terminology o We call X a random variable because it is a numerical quantity whose value depends on the outcome of a process that involves chance. o We call {1, 2, 3, 6, 10} the support of X because it is the set of values for which P( X )>0. Professor Thomas R. Professor Thomas R. 77 Plotting the Probability Distribution Professor Thomas R. Professor Thomas R. 88 Dont Do This! Professor Thomas R. Professor Thomas R. 99 Cumulative Distribution Professor Thomas R. Professor Thomas R. 1010 Dont Do This! Professor Thomas R. Professor Thomas R. 1111 Analyzing Your Payoffs o Suppose we play 6000 times. What can you expect? n Receive $1 1000 times: $1000 n Receive $2 2000 times: $4000 n Receive $3 1000 times: $3000 n Receive $6 1000 times: $6000 n Receive $10 1000 times: $10,000 o Your total payoff = $24,000 Professor Thomas R. Professor Thomas R. 1212 Is the Game Fair? o You pay $5 to play the game. o Your expected payoff is $4....
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This note was uploaded on 09/17/2009 for the course BUS 215 taught by Professor Thomassexton during the Fall '09 term at SUNY Stony Brook.

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Chapter 6 Discrete Distributions - Click to edit Master...

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