Question

The table shows the probability distribution of the number of bases for a randomly selected time at bat for a San Francisco Giants player in 2010. San Francisco Giants Hitting Number of Bases Probability

San Francisco Giants Hitting
Number of Bases	Probability
0	0.7429
1	0.1704
2	0.0517
3	0.0055
4	0.0295

a. What is the random variable X in this case?

b. Verify that the probabilities give a legitimate probability distribution.

c. Find E(X).

Answer 1

a)

Random variable X = Number of bases.

Where X takes values as 0 , 1 , 2, 3 , 4

b)

The probabilities gives valid probability distribution if sum of probabilities equal to 1

P(X) = 1

= 0.7429 + 0.1704 + 0.0517 + 0.0055 + 0.0295

= 1

Since sum of probabilities equal to 1, this is valid probability distribution.

c)

E(X) = X * P(X)

= 0 * 0.7429 + 1 * 0.1704 + 2 * 0.0517 + 3 * 0.0055 + 4* 0.0295

= 0.4083