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8 February, 00:19

The probability distribution of X, the number of imperfections per 10 meters of a synthetic fabric in continuous rolls of uniform width, is given ascol1 x 0 1 2 3 4 col2 f (x) 0.41 0.37 0.16 0.05 0.01 Find the average number of imperfections per 10 meters of this fabric.

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  1. 8 February, 00:43
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    E (X) = 0.88

    Explanation:

    The average number of imperfections to be determined is the expected value of the random variable X.

    E (X) = Σxf (x)

    X

    Of which f is the probability distribution of the random variable X.

    Thus, the needed value is:

    E (X) = Σxf (x)

    X

    = 4

    Σxf (x)

    X_0

    = 0. f (0) + 1. f (1) + 2. f (2) +

    3. f (3) + 4. f (4)

    = 0. 0.41 + 1. 0.37 + 2. 0.16 +

    3. 0.05 + 4. 0.01

    = 0.88

    E (X) = 0.88
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