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November 24th, 2010, 09:34 PM   #1
gaz
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Data Management Help Please

A computer has been programmed to draw a rectangle with perimeter of 24cm. The program randomly chooses integer lengths. What is the expected area of the rectangle?





Answer is 26cm sqaured. Required to solve this questions using uniform distribution and expected values. Thank you in advance.
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November 24th, 2010, 09:39 PM   #2
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Re: Data Management Help Please

Are you sure the answer is 26 cm. and not 36 cm.?
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November 24th, 2010, 09:40 PM   #3
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Re: Data Management Help Please

yes I am sure
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November 24th, 2010, 10:53 PM   #4
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Re: Data Management Help Please

well suppose the first line of the rec is x and the other is y then obviously 2x +2y=24 dividing by 2 we get x+y=12 now the area is obviously x*y now lets make alist of expected values
x=1 y=11 x*y=11
x=2 y=10 x*y=20
x=3 y=9 x*y=18
x=4 y=8 x*y=32
x=5 y=7 x*y=35
x=6 y=6 x*y=36
now we could give other values for x and y but we will get the same results exactly(like if x=7 and y= 5 but we already had this value)apparently 11<= x*y=<36 now to get the expected value i think(but not quite sure) u should calculate the sum of all possible square meaning 11+20+18+32+35+36 and divide by the possibilities which r 6 possibilities : the sum is 152 now 152/6=25.3333 and since u want an integer value u will probably get 26
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November 24th, 2010, 11:11 PM   #5
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Re: Data Management Help Please

Thank you.
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