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Math Help - Data Management - Prob. Help

  1. #1
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    Data Management - Prob. Help

    A computer is programmed to draw rectangles with perimeter or 24 cm. the program randomly chooses integer lengths. what is the expected area of a rectangle.

    i really dont get this one...

    It would be great if you could point me to the correct direction...

    Not begging for the answer only understanding.
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  2. #2
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    Let the width of the rectangle be x, and the length be y.

    Then 2x + 2y = 24
    x + y = 12
    y = 12 - x
    And the area = xy = x(12 - x)

    x can be all integers between and including 1 and 11.
    All the outcomes below,

    x=1, area=11
    x=2, area=20
    x=3, area=27
    x=4, area=32
    x=5, area=35
    x=6, area=36
    x=7, area=35
    x=8, area=32
    x=9, area=27
    x=10, area=20
    x=11, area=11

    Now, use E(X) = n \times p to find the solution.
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  3. #3
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    We never learnt it using that method...

    Is this a binomial distibution ?

    I think it goes with P(X) nCx . p^x . q^n-x
    p = success
    q = fail
    n = total trials
    x = successes from total trials
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  4. #4
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    I don't see how this is binomial distribution. The computer has RANDOMLY chosen the x,y values and so each value of X has equal probability.

    It is a simple distribution like this:

    Area=11, p=2/11
    Area=20, p=2/11
    Area=27, p=2/11
    Area=32, p=2/11
    Area=35, p=2/11
    Area=36, p=1/11

    This allows the expected area to be calculated relatively simply.
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  5. #5
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    I am lost...I hate questions like these.
    I am actually having trouble in *approaching* the question...
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  6. #6
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    But do you understand the method to find the answer?
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  7. #7
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    Quote Originally Posted by nzmathman View Post
    But do you understand the method to find the answer?
    The more interesting problem is when x is a continuous random variable .... (of course, in practice x is always discrete).
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