Expected Value of a Random Variable Exercise

1. The probability distribution for the discrete random variable X is given below.

x
0
1
4
P(X = x)
0.2
0.4
0.4

Calculate E(X)

2. The probability distribution for the discrete random variable Z is given below.

z
10
11
12
13
P(Z = z)
0.2
0.3
0.1
0.4

Calculate E(Z).

 

3. The probability function for a discrete random variable W is shown below.

w
-2
-1
0
1
2
P(W = w)
0.25
0.1
0.2
0.3
0.15

Calculate E(W).

4. The probability function for a discrete random variable X is shown below.

x
0
1
2
P(X = x)
0.25
0.5
0.25

Find E(X).

5. The probability distribution for X, the number of heads showing when three coins are tossed, is given below.

x
0
1
2
3
P(X = x)
1 / 8
3 / 8
3 / 8

1 / 8

What is the expected value for X?

6. The probability distribution for X the total scored when two dice are thrown is shown below.

x
2
3
4
5
6
7
8
9
10
11
12
P(X = x)
1 / 36
1 / 18
3 / 36

1 / 9

5 / 36
1 / 6
5 / 36
1 / 9
3 / 36
1 / 18
1 / 36

Find E(X)

7. The probability distribution for the random variable Y is shown below.

y
2
4
6
8
P(Y = y)
k
4k
2k
3k

a. Find the value of k

b. Find E(Y)

8. Find the expected number of tails when two fair coins are tossed.

9. A raffle has one prize of $50 and one of $20. One hundred tickets are sold. What would be the expected value (average return) on one ticket?

10. In a game of "unders and overs", two dice are tossed.

The gambler pays $2 to play and wins $10 if the total is 7.

What is the expected gain to the gambler.