Distribution of Bernoulli random variable

AI Thread Summary
The distribution of the sum of independent Bernoulli random variables, Y = ∑Ni=1 Xi, is a binomial distribution with parameters n (the number of trials) and p (the probability of success). The expected value E(Y) is calculated as np, where n is the number of Bernoulli trials and p is the probability of success for each trial. The discussion highlights the importance of understanding the relationship between Bernoulli and binomial distributions. Participants express uncertainty about deriving the expectation and seek clarification on the concepts. The conversation emphasizes the standard nature of these distributions in probability theory.
trojansc82
Messages
57
Reaction score
0

Homework Statement



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


b) Show E(Y) = np

Homework Equations



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

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.
 
Physics news on Phys.org
trojansc82 said:

Homework Statement



a) Let X1, X2, ...XN be a collection of independent Bernoulli random variables. What is the distribution of Y = \sumNi = 1 Xib) Show E(Y) = np

Homework Equations



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

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.

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?
 
LCKurtz said:
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?

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.
 
Thread 'Use greedy vertex coloring algorithm to prove the upper bound of χ'
Hi! I am struggling with the exercise I mentioned under "Homework statement". The exercise is about a specific "greedy vertex coloring algorithm". One definition (which matches what my book uses) can be found here: https://people.cs.uchicago.edu/~laci/HANDOUTS/greedycoloring.pdf Here is also a screenshot of the relevant parts of the linked PDF, i.e. the def. of the algorithm: Sadly I don't have much to show as far as a solution attempt goes, as I am stuck on how to proceed. I thought...
Back
Top