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