Let X be the number of packages being mailed by a randomly selected customer at a certai...

Let X be the number of packages being mailed by a randomly selected customer at a certain shipping facility. Suppose the distribution of X is as follows:

a. Consider a random sample of size n = 2 (two customers), and let be the sample mean number of packages shipped. Obtain the probability distribution of .

b. Refer to part (a) and calculate

c. Again consider a random sample of size n = 2, but now focus on the statistic R = the sample range (difference between the largest and smallest values in the sample). Obtain the distribution of R. [Hint: Calculate the value of R for each outcome and use the probabilities from part (a).]

d. If a random sample of size n = 4 is selected, what is