Given the following probability distribution for an infinite population with the discrete random variable, x:

a. Determine the mean and the standard deviation of x.
b. For the sample size n 5 2, determine the mean for each possible simple random sample from this population.
c. For each simple random sample identified in part (b), what is the probability that this particular sample will be selected?
d. Combining the results of parts (b) and (c), describe the sampling distribution of the mean.
e. Repeat parts (b)€“(d) using a sample size of n 5 3 instead of n 5 2. What effect does the larger sample size have on the mean of the sampling distribution? On the standard error of the sampling distribution?

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