I'm guessing that this is a geo with p=.5.
X is the trial in which the first heads appears?
D would be the variance then, also known as the dispersion.
- How many coin flips are expected for the first tail?
- is number of coin flips before first tail. What is 's dispersion, ?
- ... but what is ? The answer given is .
The expectation of a geo is 1/p.
That's easy to prove and I'm sure it's online too.
It's obvious too, since the smaller p is, the longer one should wait until the the success arrives.
Geometric distribution - Wikipedia, the free encyclopedia