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1.A balanced coin is tossed infinite number of times. The value of 1 is assigned to a head and the value of 2 is assigned

1.A balanced coin is tossed infinite number of times. The value of 1 is assigned to a head and the value of 2 is assigned to a tail. Suppose the random variable representing the number of heads in tossing.

a.Construct the probability distribution of .

b.Calculate the mean and variance of .

Suppose a sample of three coins is drawn from the above population and we calculate the mean.

c.Construct the probability distribution of the sample mean .

d.Calculate and . Show your work.

e.Refer to parts (d) and (b) and verify and .

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