CH4 - Q4.2

[Noely]

Hi All,

Sorry this might be a very silly question, but I was working through question 4.2 of the material for CS1 and can't figure out where the following happens:

var = var[E(U|V)] + E[var(U|V)] = var[1/2*V] + E[1/12*V^2]
var = 1/4*var[V] + 1/12*E[V^2]

I can't seem to figure out how the 1/4 comes about?

 

[mugono]

Hi All,

Sorry this might be a very silly question, but I was working through question 4.2 of the material for CS1 and can't figure out where the following happens:

var = var[E(U|V)] + E[var(U|V)] = var[1/2*V] + E[1/12*V^2]
var = 1/4*var[V] + 1/12*E[V^2]

I can't seem to figure out how the 1/4 comes about?

Hi

It comes from the following:

Var(aX) = a^2 Var(X)

where X is a random variable and ‘a’ is a constant.

Therefore 0.5x0.5 = 0.25.