Mathematical and Computational Modeling in Systems Engineering

 Mathematical and Computational Modeling in Systems Engineering

Show that E((X-E(X))2) = E(X 2) – E(X)2but this time only use the properties of E(.), i.e., do not break it down into a summation

Discrete random variables X1, … ,Xn  are IID (Independent and identity distributed) with distribution ‘X’ and Y1, … , Ym  are IID with distribution ‘Y’.  Alpha is a constant. Show that:

var(αX)=α^2 var(X)

var(X + Y) = var(X) + var(Y)

What assumption are we making about the variance of ‘X’ and ‘Y’?

Hint: You can use any result you have found from any previous lecture, assignment, or coursework about expectation.