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Math Help - probability

  1. #1
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    probability

    3. Determine whether each of the distributions given below represents a probability distribution. Justify answer
    a) x |1 | 2 | 3 | 4
    P(x) |1/8| 1/8| 3/8 | 1/8

    b) x | 20 | 30| 40 | 50
    P(x)| 0.3|0.2| 0.1| 0.4
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  2. #2
    MHF Contributor red_dog's Avatar
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    The sum of probabilities must be equal to 1.
    In the first "distribution" the sum is \displaystyle \frac{6}{8}\neq 1, so isn't a distribution.
    In the second the sum is equal to 1, so it is a corect distribution.
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  3. #3
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    There are two requirements:
    0 \le P(x) \le 1 and  \sum\limits_x {P(x)}  = 1.

    Now you check both of those for these properties.

    EDIT: What is the point of simply handing out simple answers?
    Is that what teaching has come to?
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  4. #4
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    Hello, Harry!

    3. Determine whether each of the distributions given below represents a probability distribution.

    a)\;\;\begin{array}{cccccccccc}x & | & 1 & | & 2 & | & 3 & | & 4 & | \\ \hline<br />
P(x) & | & \frac{1}{8} & | & \frac{1}{8} & | & \frac{3}{8} & | & \frac{1}{8} & | \end{array}
    No . . . The probabilities do not add up to 1.


    b)\;\;\begin{array}{cccccccccc} x & | & 20 & | & 30 & | & 40 & | & 50 & | \\ \hline<br />
P(x) & | & 0.3 & | & 0.2 & | & 0.1 & | & 0.4 & | \end{array}

    Yes . . . The probabilities are positive and add up to 1.

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