Question

Suppose E(x)=5 and E[x(x-1)]=27.5. What is E[x^2]?

Answer 1

you can use properties of expected value

Answer 2

http://www.rapidtables.com/math/probability/Expectation.htm

Answer 3

Properties of expectation

Linearity

When a is constant and X,Y are random variables:

E(aX) = aE(X)

E(X+Y) = E(X) + E(Y)
Constant

When c is constant:

E(c) = c
Product

When X and Y are independent random variables:

E(X *Y) = E(X) * E(Y)

Answer 4

we can use this as a guide

Answer 5

E(x)=5 and
E[x(x-1)] = 27.5

but
E[x(x-1)] =E(x^2 - x)= E(x^2) - E(x)

Answer 6

now substitute

Answer 7

E(x^2) - E(x) = 27.5

E(x^2) = 27.5 + E(x)
E(x^2) = 27.5 + 5