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 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.