I am taking a course in probability and I have trouble computing the variance of a random variable.
There are 2 cases we saw in class that I would like to understand:
First I will state the definition of variance of expected value:
- If X is a random variable who's values are in N, then
- If X is a random variable and E(X) exists, then the variance of X is:
Now here are the examples I'd like to understand:
1. binomial distribution: If X is a random variable that follows a binomial distribution of parametres n and p then we can write where the 's are bernoulli variables of parametre p. Then
2. negative binomial distribution (Pascal law): If X is a random variable that follows a pascal law of parameters r and p the where 's are independant geometric variables. Then