CFA Level 1 Exam: Random Variable Y Properties

Mean and Variance of Y

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Question

A random variable, X, has a mean of 10 and a standard deviation of 15. Another random variable, Y, is defined by Y = 2X + 3. Then, which of the following is/are true? I. The mean of Y is 33. II. The variance of Y is 30. III. The standard deviation of Y is 33. IV. X and Y are perfectly correlated.

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Explanations

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A. B. C. D. E. F. G.

Explanation

The mean of Y is 2*10 + 3 = 23. The standard deviation of Y is 2*15 = 30. Its variance is then equal to 30^2 = 900. Finally, since Y is a linear multiple of X, X and Y are perfectly correlated (positively, in this case)

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