5 Consider the population described by the probability distribution shown here:

The random variable x is observed twice. If these observations are independent, verify that the different samples of size 2 and their probabilities are as follows:

a. Find the sampling distribution of the sample mean x.

b. Construct a probability histogram for the sampling distribution of x.

c. What is the probability that x is 4.5 or larger?

d. Would you expect to observe a value of x equal to 4.5 or larger? Explain.

Transcribed Image Text:

x 1 2 3. 4 5 p(x) .2 .3 .2 .2 .1