Question

The random variables X and Y have variances 0.2 and 0.5 respectively. Let Z= 5X-2Y. Find variance of Z?

Answer 1

Answer:

Given:

The random variables X and Y have variances 0.2 and 0.5 respectively. Let Z= 5X-2Y.

To find:

The variance of Z is?

Solution:

From given, we have,

The variance of X = Var(X) = 0.2

The variance of Y = Var(Y) = 0.5

Z= 5X-2Y

The variance of Z is given by,

Var(Z) = Var(5X) - Var(2Y)

= 5 × Var(X) - 2 × Var(Y)

= 5 × 0.2 - 2 × 0.5

= 1 - 1

= 0

∴ The variance of Z = Var(Z) = 0