# Thread: expected value and variance of difference of population proportions

1. ## expected value and variance of difference of population proportions

Hi everyone,

i need help finding E(p1-p2) And Var(P1-P2) where p1=X1/n1 where n1 is a sample from group 1 that yielded X1 successes and p2=X2/n2 where n2 is a sample from group 2 that yielded X2 successes. I.E find the expected value and variance for the difference between two population proportions.

2. Originally Posted by nikie1o2
Hi everyone,

i need help finding E(p1-p2) And Var(P1-P2) where p1=X1/n1 where n1 is a sample from group 1 that yielded X1 successes and p2=X2/n2 where n2 is a sample from group 2 that yielded X2 successes. I.E find the expected value and variance for the difference between two population proportions.
Isn't the theory in your class notes or textbook? You will find what you need using google:

Google

3. You mean $\hat P$ and not p

p is an unknown constant and it has no distribution, it's mean is itself and it's variance is 0.

NOW $\hat P$ is X/n, where X is a binomial rv with sample size n and p as the probability. SO $\hat P$ is an unbiased estimator of p.

4. The variance of the difference of two estimated population proportions is expressed by the following formula:
$\hat{p}$1/n1 + $\hat{p}$2/n2
I would imagine that the expected value is just X1 - X2, but I'm not certain.

5. Originally Posted by Effendi
The variance of the difference of two estimated population proportions is expressed by the following formula:
$\hat{p}$1/n1 + $\hat{p}$2/n2
I would imagine that the expected value is just X1 - X2, but I'm not certain.
you also are mixing up statistics p-hats and parameters
thats the point of this work
To estimate UNKNOWN parameters with statistics, which are functions of the data by definition.