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# Let X represent the number of tires with low air pressure ISBN: 9780073401331 38

## Solution for problem 4E Chapter 2.4

Statistics for Engineers and Scientists | 4th Edition

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Problem 4E

Let X represent the number of tires with low air pressure on a randomly chosen car.

a. Which of the three functions below is a possible probability mass function of X? Explain.

 X 0 1 2 3 4 p1(x) 0.2 0.2 0.3 0.1 0.1 p2(x) 0.1 0.3 0.3 0.3 0.2 p3(x) 0.1 0.2 0.2 0.4 0.1

b. For the possible probability mass function, compute μX. and Step-by-Step Solution:

Step 1 of 3:

Let X denote the number of tires with low air pressure on a randomly chosen car.

 X 0 1 2 3 4 0.2 0.2 0.3 0.1 0.1 (x) 0.1 0.3 0.3 0.3 0.2 (x) 0.1 0.2 0.2 0.4 0.1

We have to find

Which of given  three functions is a possible probability mass function of X. For the possible mass function,we have to compute E(x) and V(X).

Step 2 of 3:

The probability mass function(pmf) is a function that gives the probability that a discrete random variable is exactly equal to some value.

Therefore the addition all probabilities should give a total one.

Here = 0.2+ 0.2 +0. 3 +0.1+ 0.1

= 0.9 = 1.2 = 0.1 +0.2 +0.2+ 0.4 + 0.1

=  1

So here the third one (x) is the possible probability mass function of X since other two are not giving a total of one.

Step 3 of 3

##### ISBN: 9780073401331

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