The probability of distribution of X the number of imperfect

The probability of distribution of X, the number of imperfections per 10 meters of synthetic fabric in continuous rolls of uniform width, is given as

x 0 1 2 3 4

P(X = x) 0.41 0.37 0.16 0.05 0.01

(a) Find the expectation of X

(b) Find the variance and standard deviation of X.

(c) If we further denote Z = 3x 2, what is the expectation and variance of Z?

(d) Recall that X is the number of imperfections per 10 meters. Suppose W is the number of imperfections per 100 meters. Could you estimate the expectation, variance and standard deviation for W?

Solution