Introduction to the Practice of Statistics: w/CrunchIt/EESEE Access Card
Introduction to the Practice of Statistics: w/CrunchIt/EESEE Access Card
8th Edition
ISBN: 9781464158933
Author: David S. Moore, George P. McCabe, Bruce A. Craig
Publisher: W. H. Freeman
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Chapter 12, Problem 12E

(a)

To determine

Whether the assumption of equal standard deviation should be used to analyze the provided data.

(b)

To determine

To find: The variances for the three groups.

(c)

To determine

To find: The pooled variances.

(d)

To determine

To find: The pooled standard deviation.

(e)

To determine

To explain: The reason for sp to be closer to s3 than other standard deviations.

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7. (a) Show that if A,, is an increasing sequence of measurable sets with limit A = Un An, then P(A) is an increasing sequence converging to P(A). (b) Repeat the same for a decreasing sequence. (c) Show that the following inequalities hold: P (lim inf An) lim inf P(A) ≤ lim sup P(A) ≤ P(lim sup A). (d) Using the above inequalities, show that if A, A, then P(A) + P(A).
19. (a) Define the joint distribution and joint distribution function of a bivariate ran- dom variable. (b) Define its marginal distributions and marginal distribution functions. (c) Explain how to compute the marginal distribution functions from the joint distribution function.
18. Define a bivariate random variable. Provide an example.
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