LaunchPad for Moore's Introduction to the Practice of Statistics (12 month access)
8th Edition
ISBN: 9781464133404
Author: David S. Moore, George P. McCabe, Bruce A. Craig
Publisher: W. H. Freeman
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Question
Chapter 12, Problem 37E
(a)
To determine
Whether a possible lack of normality in the data will cancel the conclusions that we might draw using ANOVA to analyze the data or not.
(b)
To determine
Whether the pooled standard deviation is applicable in these data sets or not.
(c)
To determine
To find: The degree of freedom and the P-value.
(d)
To determine
The pattern in means of groups.
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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.
Chapter 12 Solutions
LaunchPad for Moore's Introduction to the Practice of Statistics (12 month access)
Ch. 12.1 - Prob. 1UYKCh. 12.1 - Prob. 2UYKCh. 12.1 - Prob. 3UYKCh. 12.1 - Prob. 5UYKCh. 12.1 - Prob. 6UYKCh. 12.1 - Prob. 4UYKCh. 12.2 - Prob. 7UYKCh. 12.2 - Prob. 8UYKCh. 12 - Prob. 9ECh. 12 - Prob. 10E
Ch. 12 - Prob. 11ECh. 12 - Prob. 12ECh. 12 - Prob. 13ECh. 12 - Prob. 14ECh. 12 - Prob. 15ECh. 12 - Prob. 16ECh. 12 - Prob. 17ECh. 12 - Prob. 18ECh. 12 - Prob. 39ECh. 12 - Prob. 19ECh. 12 - Prob. 43ECh. 12 - Prob. 41ECh. 12 - Prob. 42ECh. 12 - Prob. 49ECh. 12 - Prob. 20ECh. 12 - Prob. 21ECh. 12 - Prob. 28ECh. 12 - Prob. 29ECh. 12 - Prob. 30ECh. 12 - Prob. 35ECh. 12 - Prob. 36ECh. 12 - Prob. 23ECh. 12 - Prob. 24ECh. 12 - Prob. 25ECh. 12 - Prob. 26ECh. 12 - Prob. 31ECh. 12 - Prob. 32ECh. 12 - Prob. 33ECh. 12 - Prob. 34ECh. 12 - Prob. 37ECh. 12 - Prob. 38ECh. 12 - Prob. 27ECh. 12 - Prob. 40ECh. 12 - Prob. 45ECh. 12 - Prob. 46ECh. 12 - Prob. 47ECh. 12 - Prob. 48ECh. 12 - Prob. 50ECh. 12 - Prob. 51ECh. 12 - Prob. 52ECh. 12 - Prob. 53ECh. 12 - Prob. 54ECh. 12 - Prob. 55ECh. 12 - Prob. 56ECh. 12 - Prob. 57ECh. 12 - Prob. 58ECh. 12 - Prob. 59ECh. 12 - Prob. 60ECh. 12 - Prob. 63ECh. 12 - Prob. 22ECh. 12 - Prob. 67ECh. 12 - Prob. 68ECh. 12 - Prob. 69ECh. 12 - Prob. 44ECh. 12 - Prob. 61ECh. 12 - Prob. 62ECh. 12 - Prob. 64ECh. 12 - Prob. 65ECh. 12 - Prob. 66E
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- 6. (a) Let (, F, P) be a probability space. Explain when a subset of ?? is measurable and why. (b) Define a probability measure. (c) Using the probability axioms, show that if AC B, then P(A) < P(B). (d) Show that P(AUB) + P(A) + P(B) in general. Write down and prove the formula for the probability of the union of two sets.arrow_forward21. Prove that: {(a, b), - sa≤barrow_forward10. (a) Define the independence of sets A, B, C. (b) Provide an example where A, B, C are pairwise independent but not mutually independent. (c) Give an example where P(AnBnC) = P(A)P(B)P(C), but the sets are not pairwise independent.arrow_forward23. State Bayes' formula. Jaching R. Machine.arrow_forward(d) Show that A, and A' are tail events.arrow_forward11. (a) Define the (mathematical and conceptual) definition of conditional probability P(A|B). (b) Explain the product law in conditional probability. (c) Explain the relation between independence and the conditional probability of two sets.arrow_forward25. Show that if X is a random variable and g(.) is a Borel measurable function, then Y = g(X) is a random variable.arrow_forward24. A factory produces items from two machines: Machine A and Machine B. Machine A produces 60% of the total items, while Machine B produces 40%. The probability that an item produced by Machine A is defective is P(D|A)=0.03. The probability that an item produced by Machine B is defective is P(D|B) = 0.05. (a) What is the probability that a randomly selected product be defective, P(D)? (b) If a randomly selected item from the production line is defective, calculate the probability that it was produced by Machine A, P(A|D).arrow_forward13. Let (, F, P) be a probability space and X a function from 2 to R. Explain when X is a random variable.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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