Suppose that Y is a discrete random variable with
- a. Do you expect the mean of W to be larger than, smaller than, or equal to µ = E(Y)? Why?
- b. Use Theorem 3.4 to express E(W) = E(2Y) in terms of µ = E(Y). Does this result agree with your answer to part (a)?
- c. Recalling that the variance is a measure of spread or dispersion, do you expect the variance of W to be larger than, smaller than, or equal to σ2 = V(Y)? Why?
- d. Use Definition 3.5 and the result in part (b) to show that
that is, W = 2Y has variance four times that of Y.
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Mathematical Statistics with Applications
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill