(Solved): 1) The probability distribution shown here describes a population of measurements that can assume ...

1) The probability distribution shown here describes a population of measurements that can assume values of $$0,2,4$$, and 6, each of which occurs with the same relative frequency: [35 Points] a. List all the different samples of $$n=2$$ measurements selected from this population. For example, $$(0,6)$$ is one possible pair of measurements; $$(2,2)$$ is another possible pair. b. Calculate the mean of each different sample listed in part a. c. If a sample of $$n=2$$ measurements is randomly selected from the population, what is the probability that a specific sample will be selected? d. Assume that a random sample of $$n=2$$ measurements is selected from the population. List the different values of $$\stackrel{?}{x}$$ found in part $$\mathbf{b}$$ and find the probability of each. Then give the sampling distribution of the sample mean $$\stackrel{?}{x}$$ in tabular form. e. Construct a probability histogram for the sampling distribution of $$\stackrel{?}{x}$$.