1. ## 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!

2. Originally Posted by Scrantones2000
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!

(Because my understanding is that X + Y = 6 and so Var(X + Y) = 0 ....)

3. Hi, X is # heads, Y=# tails.

How did you get Var (X+Y)=0? how about Var (X-Y)?

4. Originally Posted by Scrantones2000
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).