1. X and Y are two independent random variables with E(X) = 4 and E(X2) = 18, E(Y) = 3 and E2(Y) = 14.
Find the values of:
a. E(X + Y)
b. VAR(X + Y)
c. E(3X − 2Y)
d. VAR(3X − 2Y)
2. S and T are two independent random variables. E(S) = 4, VAR(S) = 2, E(T) = 6 and VAR(T) = 3
a. Find E(2S + 5T)
b. Find VAR(2S + 5T)
c. Find SD(2S + 5T)
3. W has a probability distribution as shown below
|
w
|
0
|
1
|
2
|
|
P(W = w)
|
0.2
|
0.5
|
0.3
|
a. Find E(W) and VAR(W)
b. Find P(W1 + W2 = 4) where W1 and W2 are two independent values of W.
c. Find E(W1 + W2) and VAR(W1 + W2)
d. Find P(2W = 4)
e. Find E(2W) and VAR(2W)
4. A and B are two independent random variables. E(A) = 6, VAR(A) = 0.5, E(B) = 5 and VAR(B) = 0.4
Find E(5A − 4B) and VAR(5A − 4B)
5. The probability distribution of two independent random variables X and Y are shown in the tables below.
|
x
|
1
|
2
|
3
|
y
|
2
|
3
|
4
|
|
|
P(X = x)
|
0.3
|
0.5
|
0.2
|
P(Y = y)
|
0.1
|
0.7
|
0.2
|
a. Find E(X + Y)
b. Find VAR(X + Y)
c. Find E(X − Y)
d. Find VAR(X − Y)
e. Complete the table for the probability distribution of X +Y
| x + y |
3
|
4
|
5
|
6
|
7
|
| P(X +Y = x + y) |
f. Use the table to confirm the answers to parts a. and b.
