Question

In a batch of ​pedometers, are believed to be defective. A​ quality-control engineer randomly selects units to test. Let random variable Xthe number of defective units that are among the units tested. The probability mass function ​f(x)​P(X​x) is given below. ​f(x)​{(0,​), ​(1,​), ​(2,​), ​(3,​)} Recall that the mean of a discrete random variable X with probability mass function ​f(x)​P(X​x) is given by . Find for the probability mass function above. What does this number​ represent?

Answer 1

The mean for the probability mass function is 0.64287.

Explanation:

The complete question is:

In a batch of ​28 pedometers, 3 are believed to be defective. A​ quality-control engineer randomly selects 6 units to test. Let random variable X = the number of defective units that are among the units tested.

The probability mass function ​f (x) is:

f (x)​ = {(0, 0.47009​), ​(1, 0.42308​), ​(2,​ 0.10073), ​(3, 0.00611​)}

Solution:

The mean of a discrete random variable X with probability mass function f (x) is:

`\mu=\sum\limits^(n)_(x=1){x* f(x)}`

Compute the mean for the probability mass function above as follows:

`\mu=\sum\limits^(n)_(x=1){x* f(x)}`

`=(0* 0.47009)+(1* 0.42308)+(2* 0.10073)+(3* 0.00611)\\=0+0.42308+0.20146+0.01833\\=0.64287`

Thus, the mean for the probability mass function is 0.64287.

This values represents the expected number of defective units for every 6 units tested.