# Homework Help: Distribution of Bernoulli random variable

1. Dec 9, 2011

### trojansc82

1. The problem statement, all variables and given/known data

a) Let X1, X2, ...XN be a collection of independent Bernoulli random variables. What is the distribution of Y = $\sum$Ni = 1 Xi

b) Show E(Y) = np

2. Relevant equations

Bernoulli equations f(x) = px(1-p)1-x

3. The attempt at a solution

a)X1 + X2 + .... + XN = p

b) Not sure. I'm assuming the expectation would mean when each probability is multiplied by "x", the x's go from 0 to n, meaning they represent the n.

2. Dec 9, 2011

### LCKurtz

Have you stated the question carefully and correctly? What is p? Are the independent random variables of the same distribution? Have you studied binomial distributions yet?

3. Dec 9, 2011

### trojansc82

Yeah, I have studied the binomial. I'm going back and looking at old tests before my final, so I'm trying to remember the way the solution worked.

I was easily able to derive the mean and variance from a Bernoulli distribution, but I'm having trouble with these two problems.

Also, p is the expected outcome. I'm assuming you're just deriving the mean of the Binomial distribution here, but I'm not sure how that is done.

4. Dec 9, 2011