5. Problem 5. (a) Consider a sample space C = {1, 2, 3, 4, 5, 6, 7, 8, 9), where each of these numbers are equally probable. Let A be the event all even numbers. Given A occurred. Compute directly by enumerating A the conditional probability of {1, 2, 3} given A. (b) Suppose A and B are two events that are independent. What can you say about the independence of each of the following pairs of events: (i) A and Bc y (ii) Ac and B, and (iii) Ac and Bc. Show work. (c) Let X be a continuous random variable and x be any real number, find the value P[X = x] and give reason for the answer. *Means the original problem has been modified as described.

5. Problem 5. (a) Consider a sample space C = {1, 2, 3, 4, 5, 6, 7, 8, 9), where each of these numbers are equally probable. Let A be the event all even numbers. Given A occurred. Compute directly by enumerating A the conditional probability of {1, 2, 3} given A. (b) Suppose A and B are two events that are independent. What can you say about the independence of each of the following pairs of events: (i) A and Bc y (ii) Ac and B, and (iii) Ac and Bc. Show work. (c) Let X be a continuous random variable and x be any real number, find the value P[X = x] and give reason for the answer. *Means the original problem has been modified as described.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter12: Probability

Section12.3: Conditional Probability; Independent Events; Bayes' Theorem

Problem 42E

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