MIT6_042JS10_lec36

MIT6_042JS10_lec36 - Carnival Dice Mathematics for Computer...

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1 Albert R Meyer, May 5, 2010 Mathematics for Computer Science MIT 6.042J/18.062J Great Expectations lec 13W.1 Albert R Meyer, May 5, 2010 Carnival Dice choose a number from 1 to 6, then roll 3 fair dice: win $1 for each match lose $1 if no match lec 13W.5 Albert R Meyer, May 5, 2010 Example: choose 5 , then roll 2,3,4 : lose $1 roll 5,4,6 : win $1 roll 5,4,5 : win $2 roll 5,5,5 : win $3 Carnival Dice lec 13W.6 Albert R Meyer, May 5, 2010 Carnival Dice Is this a fair game? lec 13W.7 Albert R Meyer, May 5, 2010 Carnival Dice # matches probability $ won 0 125 /216 -1 1 75 /216 1 2 15 /216 2 3 1 /216 3 lec 13W.9 Albert R Meyer, May 5, 2010 so every 216 games, expect 0 matches about 125 times 1 match about 75 times 2 matches about 15 times 3 matches about once Carnival Dice lec 13W.10
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2 Albert R Meyer, May 5, 2010 Carnival Dice So on average expect to win: NOT fair! lec 13W.12 lec 13W 12 Albert R Meyer, May 5, 2010 You can “expect” to lose 8 cents per play. Carnival Dice But you never actually lose 8 cents on any single play, this is just your average loss. lec 13W.13 Albert R Meyer, May 5, 2010 Expected Value The expected value of random variable R is the average value of R --with values weighted by their probabilities lec 13W.14 Albert R Meyer, May 5, 2010 The
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MIT6_042JS10_lec36 - Carnival Dice Mathematics for Computer...

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