Problem 7. A binomial distribution has parameters (n, p) where n is known and p is unknown. Find the method of moments estimator for p and compute its variance.

Suppose that we have disjoint normal populations A and B with equal but unknown population variances.   Suppose we plan a sample of size 12 from from population A and a sample of size 6 from population B which we will pool to form the pooled variance.  If the sample variance for the sample from population A is 25 and the sample variance for the sample from population B is 36, then what is the pooled sample variance?

We have a random variable X1 for population 1 with a mean value of 52 and standard deviation of 3. we have a random variable X2 for population 2 with a mean value of 50 and population standard deviation of 4. we obtain a random sample of 625 elements independently for both populations. what is the probability that the difference in the sample averages X1-X2 is at least 2.3?

We are running a hypothesis test to see if weight of African zebras is significantly different than that of Arabian horses. We assume weight in both populations is normally distributed and both populations have the same population variance in weight which is unknown to us, so we use the sample variances to estimate the standard error for our calculations. We have a sample of size 9 for the African zebras with mean 650 and a sample of size 16 for the Arabian horses with mean 659. If the pooled variance is 81, then what is the absolute value of the standardized test statistic for our data?