Introduction to the Practice of Statistics
9th Edition
ISBN: 9781319013387
Author: David S. Moore, George P. McCabe, Bruce A. Craig
Publisher: W. H. Freeman
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Chapter 13.1, Problem 2UYK
(a)
To determine
To test: Whether it is reasonable to pool the standard deviation or not.
(b)
To determine
To find: The estimate of ANOVA model parameters.
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10. (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.
23. State Bayes' formula.
Jaching R. Machine.
(d) Show that A, and A' are tail events.
Chapter 13 Solutions
Introduction to the Practice of Statistics
Ch. 13.1 - Prob. 1UYKCh. 13.1 - Prob. 2UYKCh. 13.1 - Prob. 3UYKCh. 13.1 - Prob. 4UYKCh. 13 - Prob. 5ECh. 13 - Prob. 6ECh. 13 - Prob. 7ECh. 13 - Prob. 8ECh. 13 - Prob. 9ECh. 13 - Prob. 10E
Ch. 13 - Prob. 11ECh. 13 - Prob. 12ECh. 13 - Prob. 13ECh. 13 - Prob. 14ECh. 13 - Prob. 15ECh. 13 - Prob. 16ECh. 13 - Prob. 17ECh. 13 - Prob. 18ECh. 13 - Prob. 19ECh. 13 - Prob. 20ECh. 13 - Prob. 21ECh. 13 - Prob. 22ECh. 13 - Prob. 23ECh. 13 - Prob. 24ECh. 13 - Prob. 25ECh. 13 - Prob. 26ECh. 13 - Prob. 27ECh. 13 - Prob. 28ECh. 13 - Prob. 29ECh. 13 - Prob. 30ECh. 13 - Prob. 31ECh. 13 - Prob. 32ECh. 13 - Prob. 33ECh. 13 - Prob. 34ECh. 13 - Prob. 35ECh. 13 - Prob. 36ECh. 13 - Prob. 37ECh. 13 - Prob. 38ECh. 13 - Prob. 39ECh. 13 - Prob. 40ECh. 13 - Prob. 41ECh. 13 - Prob. 42ECh. 13 - Prob. 43ECh. 13 - Prob. 44ECh. 13 - Prob. 45ECh. 13 - Prob. 46ECh. 13 - Prob. 47ECh. 13 - Prob. 48ECh. 13 - Prob. 49ECh. 13 - Prob. 50ECh. 13 - Prob. 51ECh. 13 - Prob. 52ECh. 13 - Prob. 53ECh. 13 - Prob. 54ECh. 13 - Prob. 55ECh. 13 - Prob. 56ECh. 13 - Prob. 57ECh. 13 - Prob. 58ECh. 13 - Prob. 59ECh. 13 - Prob. 60E
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- 11. (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_forward12. (a) Explain tail events and the tail o-field. Give an example. (b) State (without proof) the Kolmogorov zero-one law.arrow_forward14. Define X-¹(H) for a given HER. Provide a simple example.arrow_forward
- 9. Define a 7-system. Show that P = {(0, x]; (0, 1]} is a л-system.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_forward
- (c) Show that A is the limit of a decreasing sequence and A, is the limit of an increasing sequence of sets.arrow_forward3. Let A (-1, 1-1) for even n, and A, -(+) for odd n. Derive lim sup A, and lim inf Aarrow_forward1. Let 2 (a, b, c} be the sample space. the power sot of O (c) Show that F= {0, 2, {a, b}, {b, c}, {b}} is not a σ-field. Add some elements to make it a σ-field.arrow_forward
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