Suppose a quality control expert examines iterms for defects in a series of independent fixates, each of a fixed duration, and suppose that defects are present. Let p be the probability that the defect or flaw is detected and 1-p the probability that a defect or flaw is not detected. Let the r.v. X = the number of defects detected in n fixations. a. What is the pmf of X? b. What is the expected value of X = E(X)? c. What is the moment generating function (mgf) for the r.v. X (Remember to state the interval of validity for t)? d. Use it to find the Variance of X.
Suppose a quality control expert examines iterms for defects in a series of independent fixates, each of a fixed duration, and suppose that defects are present. Let p be the
a. What is the pmf of X?
b. What is the
c. What is the moment generating
d. Use it to find the Variance of X.
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It is given that an expert is examining items in a series of independent fixates. p is the probability that the item is defected and detected while 1-p is the probability that an item is defect but does not detected.
Consider that X is a random variable defined as the number of detected in n fixations.
Thus,
a)
The p.m.f of X can be defined as:
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