1. ## How many coin flips until first tail (or head)

1. How many coin flips are expected for the first tail?
2. $\displaystyle X$ is number of coin flips before first tail. What is $\displaystyle X$'s dispersion, $\displaystyle D(X)$?
1. $\displaystyle \sum_{i=0}^\infty \frac{1}{2^i} = 2$
2. $\displaystyle D(X)=E(X-E(X))^2=E(X^2)-(E(X))^2$ ... but what is $\displaystyle E(X^2)$? The answer given is $\displaystyle 2$.

2. 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.

3. Yes, but how do you get $\displaystyle 2$ (which is the answer) for the second point/question?

4. 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
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1. How many coin flips are expected for the first tail?
2. $\displaystyle X$ is number of coin flips before first tail. What is $\displaystyle D(X)$?
1. $\displaystyle \sum_{i=0}^\infty \frac{1}{2^i} = 2$ Solved this one.
2. Don't know how to find dispersion.