3. A certain industrial process is brought down for recalibration whenever the q

Question

3. A certain industrial process is brought down for recalibration whenever the quality of the items produced falls below specifications. Let X represent the number of times the process is recalibrated during a week, and assume X has the probability mass function shown below. Find the mean of X.

                   X       |         0        1        2        3        4

                   P(X) |     0.35     0.25   0.20   0.15    0.05

b. Find the variance for the random variable X described in problem #3. (Use short cut).

Explanation / Answer

a.In order to find the mean (expectation) of the given distribution, we will use the following formula:

=xp(x)

So, first we need to multiply each value of X by each probability P(X), then add these results together. In this example we have:

=13/10.

b.Now we will find the sum:

x2p(x)=16/5

So variance is x2p(x) - mean2=151/100

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