Let P(A) = p, P(A | B) = q, P(B | A) = r. Find relations between the number p, q, r forthe following cases:(a) Events A and B are mutually exclusive.(b) A and B are mutually exclusive and collectively exhaustive.(c) A is sub-event of B; B is a sub-event of A.(d) A and B are mutually exclusive.

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Answered: Let P(A) = p, P(A | B) = q, P(B | A) =…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Two fair dice are tossed, one red and one green. Let A be the event that the sum of the two dice is a 7. Let B be the event that the number on the green die is one more than the number on the red. Let C be the event that the number on the red die is 2. (i) Are A & B disjoint? (ii) Are A & B independent? (iii) Are A & C disjoint? (iv) Are A & C independent? (v) Are B & C disjoint? (vi) Are B & C independent? justify each
2. Suppose S = {1,2,3,4,5,6,7,8,9,10} and let A = {1,2,3,4,5}, B = {4,5,6,7,8}, and C = {7,9}. Find the following probabilities:
If P(A A. B. C. D. B) = 0 A and B are P(A) + P(B) = 1 independent events. A and B are mutually exclusive events. either P(A) = 0 or P(B) = 0.
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) Suppose that events A and B are independent. Show that p(A | B) + p(B)(1-p(A)) - P(A ∪ B) = 0.
(d) P(N and W) P(M and W) (e) P(N or M). Are the events N = no reaction and M = mild reaction mutually exclusive? Explain. No. P(N or M) ≠ 0. No. P(N and M) ≠ 0. Yes. P(N and M) = 0. Yes. P(N or M) = 0. (f) Are the events N = no reaction and W = washing oil off within 5 minutes independent? Explain. No. P(N and W) = P(N) · P(W). Yes. P(N and W) ≠ P(N) · P(W). No. P(N and W) ≠ P(N) · P(W). Yes. P(N and W) = P(N) · P(W).
Determine if events A and B are independent. 7 P(A and B) 20 7 13 P(B) : 20 13 P(A and B) 20 169 4) = P(B) = 2) P(A) = 100 400 7 3) Р(A) %—D 10 P(B) = 5 21 1 P(B) 1 P(A and B) 5 1 P(A and B) 4) Р(A) — 100 25
Let A and B be two events with P(A and Bc) = 1. Find P(B). Recall that Bc denotes the complement of the event B.
Suppose that in a large university, 40% of students work part time, 10% are part of one of the university's sports teams, and 5% both work part time and are part of one of the university's sports teams. Let W be the event that a student works part time, and V be the event that a student is part of one of the university's sports teams. Make sure all your answers are expressed in terms of the events W and V,. 4. А. What is the probability that a randomly selected student works part time or is a part of one of the university's sports teams? В. teams? What proportion of students do not work part time but are part of one of the university's sports С. Are W and V independent events? D. If a student works part time, what is the probability they are also part of one of the university's sports teams? Е. What proportion of students are not part of any of the university's sports teams and work part time?
Problem 4: Show that the moment generating function of random variable X N(u, o2) is equal to 1 Mx(t)ete2 You may use the fact that Mz(t) = eit", where Z ~ N(0,1)

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Let P(A) = p, P(A | B) = q, P(B | A) = r. Find relations between the number p, q, r for the following cases: (a) Events A and B are mutually exclusive. (b) A and B are mutually exclusive and collectively exhaustive. (c) A is sub-event of B; B is a sub-event of A. (d) A and B are mutually exclusive.