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Transformation of functions

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You have been given the sample {0.28, 0.09, 0.22, 0.29, 0.25, 0.68, 0.11, 0.07, 0.02, 0.54} drawn from a population distributed according to .....

(a) Suppose that, for the sample provided, the sample mean is less than the population mean. What does this imply about θ?

(b) Suppose that you are further told that, for the sample provided, the sample variance is more than the population variance. How does this additional information change your answer to (a)?

(c) What is the distribution of y = x2 given f(x) above?
(d) What is the probability that x = 0.62 given f(x) above?

See attachment for formulas.

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Solution Summary

This solution contains step-by-step calculations to determine the mean of the distribution using the variance, distribution of the formula and the probability of f(x).

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You have been given the sample {0.28, 0.09, 0.22, 0.29, 0.25, 0.68, 0.11, 0.07, 0.02, 0.54} drawn from a population distributed according to
(please see the attached file)

For this problem you may use the following result without deriving it explicitly:
(please see the attached file)

(a) Suppose that, for the sample provided, the sample mean is less than the population mean. What does this imply about θ?

Here given ...

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