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.

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

the abdomen (less formally called the belly, stomach, tummy or midriff) constitutes the part of the body between the thorax (chest) and pelvis, in humans and in other vertebrates. the region occupied by the abdomen is termed the abdominal cavity. the stomach secretes acid and enzymes that digest food. ridges of muscle tissue called rugae line the stomach. the stomach muscles contract periodically, churning food to enhance digestion. the pyloric sphincter is a muscular valve that opens to allow food to pass from the stomach to the small intestine.