Linear Combinations of Random Variables

If Z and W are independent random variables with means 2 and 3 respectively, find the mean of the linear combination 3Z - 2W.

• 0

• -1

• 4

• 5

Determine the variance of the linear combination 2X + 3Y if Var(X) = 4 and Var(Y) = 9.

• 97

• 25

• 13

• 36

If X and Y are uncorrelated random variables with Var(X) = 5 and Var(Y) = 3, calculate the variance of 4X + Y.

• 83

• 17

• 35

• 12

Find the expected value of the linear combination 2X - Y if E(X) = 3 and E(Y) = 1.

• 4

• 6

• 0

• 5

Given X and Y are normally distributed random variables with means 1 and 2, and variances 4 and 9 respectively, find the mean of the linear combination 2X + Y.

• 5

• 6

• 3

• 4

If X and Y are independent random variables with Var(X) = 2 and Var(Y) = 3, find the variance of the linear combination 4X + 5Y.

• 23

• 107

• 12

• 56

If E(X) = 12, Var(X) = 3, E(Y) = 10, Var(Y) = 4, then find Mean and variance of T = X1 + X2 - 2Y

• Mean = 4

  Variance = 81

• Mean = -8

  Variance = 49

• Mean = 4

  Variance = 22

• Mean = -8

  Variance = 22

Determine the variance of the linear combination 3U + 4V if Var(U) = 8 and Var(V) = 5.

• 59

• 37

• 23

• 44

Calculate the variance of the linear combination 5X + 2Y if Var(X) = 6 and Var(Y) = 7.

• 47

• 34

• 19

• 56

If A and B are independent random variables with Var(A) = 3 and Var(B) = 4, determine the variance of the linear combination 2A + 3B.

• 17

• 24

• 11

• 7