Question

Show that var(x-y) = var(x) var(y) - 2cov(x,y)?

Answer 1

The given question asks to show that var(x-y) = var(x) var(y) - 2cov(x,y). To prove this, we'll use the properties of variance and covariance.

Step-by-step explanation:

The given question asks to show that var(x-y) = var(x) var(y) - 2cov(x,y). To prove this, we'll use the properties of variance and covariance. Let's start by expanding both sides of the equation.

Left side:

var(x-y) = var(x+y) = E[(x-y)^2] - [E(x-y)]^2

Right side:

var(x) var(y) - 2cov(x,y) = [E(x)^2 - [E(x)]^2] * [E(y)^2 - [E(y)]^2] - 2cov(x,y)

Next, we'll simplify each side and show that they are equal.