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Math Help - Binomial variance

  1. #1
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    Binomial variance

    I'm trying to understand a problem involving a coin being thrown 6 times and either being heads or tails.

    I understand how to get the variance of X (heads) and Y (tails), mean n*p*(1-p). But how do I get the Variance of (X+Y)? I don't know how to find the covariance either. I don't know what to use for the x and y values.

    Thanks!
    Last edited by mr fantastic; September 14th 2009 at 04:03 AM.
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  2. #2
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    Quote Originally Posted by Scrantones2000 View Post
    I'm trying to understand a problem involving a coin being thrown 6 times and either being heads or tails.

    I understand how to get the variance of X (heads) and Y (tails), mean n*p*(1-p). But how do I get the Variance of (X+Y)? I don't know how to find the covariance either. I don't know what to use for the x and y values.

    Thanks!
    Please define X and Y.

    (Because my understanding is that X + Y = 6 and so Var(X + Y) = 0 ....)
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    Hi, X is # heads, Y=# tails.

    How did you get Var (X+Y)=0? how about Var (X-Y)?
    Last edited by mr fantastic; September 15th 2009 at 02:12 AM. Reason: Merged posts
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    Quote Originally Posted by Scrantones2000 View Post
    Hi, X is # heads, Y=# tails.

    How did you get Var (X+Y)=0? how about Var (X-Y)?
    If a coin is tossed n times then the number of heads plus the number of tails is clearly equal to n (assuming the coin doesn't land on its edge). That is, X + Y = n and you should know that the variance of a constant is zero.

    The obvious way of calculating Var(X - Y), at least when n is small (eg. n = 6), is to define the random variable W = X - Y and construct a probability table for W. What values can W have? What is the probability of each of those values?

    Once you've made this table, use it to calculate E(W) and E(W^2) and substitute those answers into the definition of Var(W).
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