Question

A project has a 50% chance of doubling your investment in 1 year and a 50% chance of losing half your money. what is the expected return on this investment project? what is the standard deviation of returns?

Answer 1

Let X be the random variable. 
We have:
$P(X=2x)=\dfrac{1}{2}$
$P(X=\dfrac{x}{2})=\dfrac{1}{2}$
Compute the mean like this:
$2x\times \frac{1}{2}+ \frac{x}{2}\times \frac{1}{2}= \frac{5}{4}x$
It is the expected return. 
First compute the following: $E(X)^2= \frac{25}{16}x^2$
Then $E(X^2)=(2x)^2\times \frac{1}{2}+ (\frac{x}{2})^2\times \frac{1}{2}= \frac{17}{8}x^2$
Finally the standard deviation:
$\sqrt{\frac{17}{8}x^2- \frac{25}{16}x^2}= \frac{3}{4}x$