Question

1. The discrete random variable X is the number of passengers waiting at a bus stop. The table below shows the probability distribution for X. What is the expected value E(X) for this distribution?

X	0	1	2	3	Total
P(X)	.20	.40	.30	.10	1.00

Answer the following questions using the given probability distribution.

1. Expected value E(X) of the number of passengers waiting at the bus stop.
2. Probability that there is at least 1 passenger at the bus stop.
3. Probability that there are less than 2 passengers at the bus stop.

Answer 1

Solution:

Given:The discrete random variable X is the number of passengers waiting at a bus stop.

The table below shows the probability distribution for X.

X	P(X)
0	0.2
1	0.4
2	0.3
3	0.1
Total	1.0

Part a) Expected value E(X) of the number of passengers waiting at the bus stop.

Thus we need to make following table:

X	P(X)	X*P(X)
0	0.2	0
1	0.4	0.4
2	0.3	0.6
3	0.1	0.3
Total	1

Thus

Thus Expected value E(X) of the number of passengers waiting at the bus stop is 1.3.

Part b) Probability that there is at least 1 passenger at the bus stop.

Part c) Probability that there are less than 2 passengers at the bus stop.