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## Homework Statement

suppose that 50 random samples of size n = 10 are to be taken from a population having the discrete uniform distribution

f(x) = 1/10 for x = 0,1,2,...,9

0 elsewhere

sampling is with replacement so that we are sampling from an infinite population. we get 50 random samples whose means are ... (they list 50 means)

suppose that we convert the 50 samples into 25 samples of size n = 20 by combining the first two, the next two and so on, find the means of these samples and calculate their mean and their standard deviation. compare this mean and this standard deviation with the corresponding values expected in accordance with following theorem: if a random sample of size n is taken from a population having the mean μ and variance σ^2 , then X is a random variable whose distribution has the mean μ. for samples from infinite populations the variance of this distribution is σ^2/n

## The Attempt at a Solution

I just want to make sure my method is correct. for each of the two means i am "combining" I think what they mean by combining is to find the mean of the two means to be combined. So if the first two means out of the 50 that they list are 4.4 and 3.2 , i combine them by finding the mean (4.4+3.2)/2 = 3.8 and now this is a mean of a sample of size 20 instead of 10. Once I combine the 50 samples into 25 samples this way, I find the mean and standard deviation of the 25 samples using the formulas μ = Σx/n and σ^2 = Σ(x-μ)^2/(n-1) . Then they want me to compare these with the ones I get from the theorem. I find these by using

μ = Σ(from 0 to 9) x(1/10) = 4.5

and

σ^2 = Σ(from 0 to 9)(x-4.5)^2(1/10) = 8.25

since n = 20 the variance is

8.25/20 = .4125

am i doing this the right way?