Could someone please help me with these? I am a new member, so I had to hyperlink my pdf function. Please provide me with answer, I have an assasement test very soon.
A continuous random variable x has a probability density function:
\[ \mathrm{pdf}(x) = \frac{\exp\left(-\frac{(x-3)^2}{16}\right)}{\sqrt{16\pi}}, \qquad x\in (-\infty, \infty) \]
a) Find the expected value, variance and the standard deviation of continuous random variable.
b) Find the expected value of a random variable $\exp(-x/2)$