Question

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.

Answer 1

Answer:

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