Question

Let X1, X2, ..., X64 be i.i.d. random variables from Normal (μ =-4, σ2=25, n=64).
(a) Compute E[-2X2-3X3]=

Answer 1

Is that
\[E\bigg[-2X_2-3X_3\bigg]~~?\]

Answer 2

yes

Answer 3

Okay, the expected value operator is linear, which means you can rewrite the expression as
\[E\bigg[-2X_2-3X_3\bigg]=-2E\bigg[X_2\bigg]-3E\bigg[X_3\bigg]\]
For any of these random variables, you have \(E(X)=-4\), so
\[-2E\bigg[X_2\bigg]-3E\bigg[X_3\bigg]=-2(-4)-3(-4)=20\]

Answer 4

thank you.