SIXworkbook - Expectation We need a method for summarizing...

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Expectation We need a method for summarizing the outcomes of  a process that occurs in probability. Any process in which outcomes occur in probability  is a  stochastic process. To summarize the outcome of a stochastic process,  we will associate a number with each outcome. We will then summarize the process by computing  the expected value. Weight each outcome by its  probability. We will also measure the dispersion of the outcomes  of the stochastic process with a standard deviation. Applications:  games, gambling, investments,  insurance, life.
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Fig 6.1 Page 2 Cecil Chang Net Probability Profit Whizzy Carom ($50,000) 0.10 0.05 ($25,000) 0.10 0.05 $0  0.10 0.20 $25,000  0.20 0.25 $50,000  0.25 0.25 $100,000  0.15 0.05 $150,000  0.10 0.15 The table indicates the probability of achieving specific levels of  profit for each investment.  The probabilities sum to 1.00.   Cecil Chang,  a venture capitalist, is considering two  alternative investments in start-up software businesses.   Whizzy  will offer interactive material for children,  kindergarten through the fourth grade, on the World Wide  Web on a subscription basis as a monthly electronic  magazine. Carom  will present a new game every other month aimed  at teenagers.  The games will involve multiple players  linked by the Word Wide Web.  Revenues will come from  modest subscription rates and from advertising. Cecil assesses the probabilities for profit from each  venture in the table above  Cecil will invest $50,000 in one  or the other venture and the profits shown are those he 
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Fig 6.1 Page 3 or the other venture and the profits shown are those he  expects to reap from his equity stake. Cecil says:  "In evaluating an investment, I weigh the  promise of a high return against the risk.  These two  ventures have some capable software engineering talent  and good marketing/revenue plans.  My $50,000  investment, together with the funds from the principals,  should be enough to bring the product to market and  achieve profitability if that's going to happen." Which venture is better?
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Fig 6.2 Page 4 Random Variable Assign a number to each outcome in the univer Here are three random variables associated with the roll of one die. color A B C number  dollar Contestant on each values for Numbers face a game blue 1 ($2) 27 red 2 ($2) 8 green 3 ($2) 31 yellow 4 $0  42 orange 5 $1  17 purple 6 $4  40  Numbers may be assigned to  random events in any way that is  useful in a given setting or in a  completely arbitrary fashion.
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Fig 6.2 Page 5 rse.
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Fig 6.3 Page 6 Expected Value Roll one die. x
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SIXworkbook - Expectation We need a method for summarizing...

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