Results 1 to 2 of 2

Math Help - Expected Value/Variance, multivariate

  1. #1
    Newbie
    Joined
    Mar 2009
    Posts
    5

    Expected Value/Variance, multivariate

    Suppose that tosses of a biased coin which come sup heads with probability 1/4 are independent. The coin is tossed 40 times and the number of heads X is counted. The coin is then tossed X more times.
    a) Determine the expected total number of heads.
    b) Determine the variance of the total number of heads.

    My solution so far:
    Let X1 be the total number of heads after the 40 first tosses. Let X2 be the total number of heads in the next set of tosses.

    a) X1 ~ bin(1/4, 40) and X2 ~bin(1/4, x1)

    E(X1 + X2) = E(X1) + E(X2) = 10 + 2.5 = 12.5

    b) I am stuck here. If I use
    var(X1+X2) = var(X1) + var(X2) +2cov(X1,X2)

    How can I get cov(X1,X2)?
    Cov[X,Y] = E[X1X2]-E[X1]E[X2] But what is E[X1X2]?

    If I made a mistake in the first part please let me know about that too.
    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by EitanG View Post
    Suppose that tosses of a biased coin which come sup heads with probability 1/4 are independent. The coin is tossed 40 times and the number of heads X is counted. The coin is then tossed X more times.
    a) Determine the expected total number of heads.
    b) Determine the variance of the total number of heads.

    My solution so far:
    Let X1 be the total number of heads after the 40 first tosses. Let X2 be the total number of heads in the next set of tosses.

    a) X1 ~ bin(1/4, 40) and X2 ~bin(1/4, x1)

    E(X1 + X2) = E(X1) + E(X2) = 10 + 2.5 = 12.5

    b) I am stuck here. If I use
    var(X1+X2) = var(X1) + var(X2) +2cov(X1,X2)

    How can I get cov(X1,X2)?
    Cov[X,Y] = E[X1X2]-E[X1]E[X2] But what is E[X1X2]?

    If I made a mistake in the first part please let me know about that too.
    Thanks
    I can't help right now but I will note for others reading this thread that E(X_2) = \frac{10}{4} can be found by first defining X_2 = \sum_{i = 1}^{X_1} Y_i where Y_i is a Bernoulli random variable and then using Wald's equation.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Expected Value and Variance?
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: November 8th 2011, 12:00 PM
  2. Expected Value and Variance
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: May 10th 2010, 04:24 AM
  3. Expected value and variance
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: March 9th 2010, 10:30 PM
  4. multivariate statistics ; compute variance
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: October 20th 2009, 04:30 PM
  5. expected and variance
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: July 9th 2007, 12:53 PM

Search Tags


/mathhelpforum @mathhelpforum