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 VAR(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 VAR(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 the standard deviation of W, SD(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 VAR(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 variance of 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 the standard deviation, SD(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)
c. Find VAR(X)
8. Find the variance of the probability function of the number of tails when two fair coins are tossed.
