1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Flipping a coin, length of runs

  1. Dec 4, 2011 #1
    1. The problem statement, all variables and given/known data

    We flip a biased coin (the probability of a head is p, the probability of a tail is q=1-p). Denote X and Y the length of the first and the second run. A "run" is a maximal sequence of consecutive flips that are all the same. For example, if the sequence is HHHTHH... , then X=4, Y=1, if the sequence is THHTHTH..., then X=1, Y=2. Find the followings: E(X), E(Y), E(X^2), E(Y^2), Var(X), Var(Y), Cov(X, Y).

    2. Relevant equations

    3. The attempt at a solution

    I am quite unsure, but I think we should use conditional expeted value conditioning with the result of the first toss. I suppose that to calculate Cov(X, Y) we should use the law of total covariance.

    I would be really grateful if you could help me!
    Last edited: Dec 4, 2011
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted