The probability of distribution of X, the number of imperfections per 10 meters
ID: 3379601 • Letter: T
Question
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?
Explanation / Answer
The probability of distribution of X, the number of imperfections per 10 meters
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