Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Hi all,

I want to compute the variance of a variable that is defined at each step as a recursion of binomials in the following way:

A=1

B=Bin(1,A)*Bin(1,p)

C=Bin(1,B)*Bin(1,p)

D=Bin(1,C)*Bin(1,p), etc...

Generalized form:

X(T+1)=Bin(1,X(T))*Bin(1,p);

Question: variance(X(T))=?

maybe it is too easy, but I would really appreciate some help...

Thanks in advance

share|improve this question
    
I think you need to clarify the question. "Bin(1,p)" would usually mean the probability distribution of the number of successes in just one trial (so the number of successes must be 0 or 1) with probability p of success on each trial. But what does "Bin(1,C)" mean, if C is an integer that may be bigger than 1, so it cannot be a probability? –  Michael Hardy May 3 '11 at 19:37
add comment

1 Answer 1

It seems each $X(T)$ is Bernoulli, that is $X(T)=0$ or $1$ almost surely. As such, the variance of $X(T)$ is $a(T)(1-a(T))$ where $a(T)=E(X(T))$. But $a(0)=1$ and $a(T+1)=a(T)p$ hence $a(T)=p^T$ and the variance of $X(T)$ is $p^T(1-p^T)$.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.