Linear transformations

In this section, we concentrate on a random variable that is defined as a linear transformation of another.

Mean and variance

If \(X\) is a random variable and \(a\) and \(b\) are constants, then the random variable \(Y = a + bX\) has the following mean and variance.

\[ \begin{align} E[Y] &= a + b \times E[X] \\[0.4em] Var(Y) &= b^2 \times Var(X) \end{align} \]

(Proved in full version)