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

• Sep 15th 2010, 09:05 AM
courteous
How many coin flips until first tail (or head)
Quote:

1. How many coin flips are expected for the first tail?
2. $X$ is number of coin flips before first tail. What is $X$'s dispersion, $D(X)$?

1. $\sum_{i=0}^\infty \frac{1}{2^i} = 2$
2. $D(X)=E(X-E(X))^2=E(X^2)-(E(X))^2$ ... but what is $E(X^2)$? The answer given is $2$.
• Sep 17th 2010, 11:32 PM
matheagle
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.
• Sep 18th 2010, 07:02 AM
courteous
Yes, but how do you get $2$ (which is the answer) for the second point/question?
• Sep 18th 2010, 07:06 AM
matheagle
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
http://cnx.org/content/m13124/latest/
• Sep 18th 2010, 07:51 AM
courteous
Quote:

1. How many coin flips are expected for the first tail?
2. $X$ is number of coin flips before first tail. What is $D(X)$?

1. $\sum_{i=0}^\infty \frac{1}{2^i} = 2$ Solved this one. (Nod)
2. Don't know how to find dispersion.