Expected value and variance of linear function

When $h\left(X\right)=aX+b,$ the expected value and variance of $h\left(X\right)$ satisfy the same properties as in the discrete case: $E\left[h\left(X\right)\right]=a\mu +b$ and $V\left[h\left(X\right)\right]=a^2\cdot {\sigma }^2.$