# Math Help - help me pliz

1. ## help me pliz

how to derive mean ang variance for normal distribution???????????

2. Originally Posted by students
how to derive mean ang variance for normal distribution???????????
$E(X) = \frac{1}{\sigma \sqrt{\pi}} \int_{-\infty}^{+\infty} x \, e^{\frac{(x - \mu)^2}{2 \sigma^2}} \, dx = \mu$.

$\text{Var}(X) = E\left(X^2\right) - \mu^2 = \sigma^2$.

Note that $E\left(X^2\right) = \frac{1}{\sigma \sqrt{\pi}} \int_{-\infty}^{+\infty} x^2 \, e^{\frac{(x - \mu)^2}{2 \sigma^2}} \, dx = \sigma^2 + \mu^2$.

You'll find the details of the actual calculations in most mathematical statistics textbooks.