Complete the table below. Based on the data in the table above, what is the mean

Question

Complete the table below. Based on the data in the table above, what is the mean of x? Based on the data in the table above, what is the standard deviation of x? A quality engineer inspects completed parts as they are exiting the assembly line. The probability of a part containing 0, 1, 2, or 3 defects is shown below. P(X = 0) = 0.30 P(X = 1) = 0.35 P(X = 2) = 0.25 P(X = 3) = 0.10 Based on these probabilities, what is the value of F(2.75)? In a semiconductor manufacturing process, four wafers from a lot are tested. Each wafer is classified as pass or fail. Assume the probability that a wafer passes the test is 0.90 and that wafers are independent. Determine the probability mass function of wafers from a lot that pass the test. Determine the cumulative distribution function for the random variable in exercise 3. Calculate the mean, variance, and standard deviation of the random variable in exercise 3.

Explanation / Answer

A) Mean of X = Expectation, E(x) = 0x0.2 + 0.1x1 + 0.3x2 + 0.1x3 + 0.3x4

= 0.1 + 0.6 + 0.3 + 1.2 = 2.2

B) variance = sum of {(xi - E(x))2 * p(x)}

= 0+(1-2.2)2x0.1 + (2-2.2)2x0.3 + (3-2.2)2x0.1 + (4-2.2)2x0.3

= 0.144+0.012+0.064+0.972

= 1.192

So, standard deviation = square root of 1.192 = 1.09

X 0 1 2 3 4 f(x) 0.2 0.1 0.3 0.1 0.3 F(x) 0.2 0.3 0.6 0.7 1

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