sec_5_2_sol

sec_5_2_sol - the message is 2, For example, is thereFore...

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APPM 4/5570 Solutions to Problems from Section 5.2 24. Let’s make a table where A ’s possible seat numbers go down the rows and B ’s possible seat numbers go down the columns. We will fll this table with the number oF people who will handle the message For each case. (Note that we can’t put A and B in the same seat, so there will be some blank spots in the table.) 1 2 3 4 5 6 1 - 2 3 4 3 2 2 2 - 2 3 4 3 3 3 2 - 2 3 4 4 4 3 2 - 2 3 5 3 4 3 2 - 2 6 2 3 4 3 2 - There are 30 possible places For A and B to be sitting, all oF which are equally likely, so the probability that they are sitting in any one oF the confgurations shown in the table is 1 / 30. The probability that the number oF people to handle
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Unformatted text preview: the message is 2, For example, is thereFore 12 / 30. Overall, we have # people 2 3 4 prob. 12 / 30 12 / 30 6 / 30 and so the expected number oF people to handle the message is (2)(12 / 30) + (3)(12 / 30) + (4)(6 / 30) = 84 / 30 = 2 . 8 . 25. The expected value oF a uniForm random variable on [ a, b ] is right in the center at ( a + b ) / 2. or a uniForm random variable on [ L-A, L + A ], the center is at L . ThereFore E [ X ] = L and E [ Y ] = L . E [area] = E [ XY ] indep = E [ X ] E [ Y ] = L L = L 2 ....
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