9. Suppose (An} are independent events satisfying P(An) < 1, for all n. Show8P(An) = 1 iff P(An i.o. ) = 1.n=1Give an example to show that the condition P(An) < 1 cannot be dropped.

Answered: Image /qna-images/answer/e7084b2d-7765-4ce5-844d-f53ebd615c3d.jpg

Answered: 9. Suppose (An) are independent events…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

8
8. Let A, B be two events with P(A) = ½, P(A − B) = 3, determine P(AB).
It doesn’t show the last parts (e) P(N or M) Are the events N= no reaction and M= mild reaction mutually exclusive? Explain. Yes. P(N and M) = 0. Yes P(N or M) = 0. No. P(N or M) ≠ 0. No. P(N or M) ≠ 0. (f) Are the events N = no reaction and W= washing oil off within 5 minutes independent? Explain. 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). No. P(N and W) = P(N) • P(W).
5. Let = {x|0 ≤ x ≤ 2}, A = {x | 0.5 < x≤ 1}, B = {x | 0.75 ≤ x < 1.5}, determine the following events: (1) AB; (2) AUB; (3) A B; (4) AB.
2. A number U is selected at random between 0 and 1. Let the events A and B be "U differs from 1/2 by more than 1/4" and "1-U is less than 1/2", respectively. Find the events An B, Ān B, AU B.
Assume A and B are independent events with P(A) = 0.42 and P(B) = 0.65. Find (a) P(A n B), (b) P(AUB), (c) P (A'n B'), (d) P (A'n B), and (e) P(ANB'). ... (a) P(An B) = (Type an integer or a decimal.) (b) P(A U B) = (Type an integer or a decimal.) (c) P (A'n B') = (Type an integer or a decimal.) (d) P (A' n B) = (Type an integer or a decimal.) (e) P (An B') = (Type an integer or a decimal.)
4. Let A und B be two events such that: P(A)=0.48. P(B)=0.67 and P(AnB)=0.22 Then P(AUB) = a) 0.55 b) 0.93 c) 0.26 d) 0.87
Assume A and B are independent events with P(A) = 0.14 and P(B) = 0.55. Find (a) P(A N B), (b) P(A U B), (c) P (A'n B'), (d) P (A' N B), and (e) P (ANB'). ..... (a) P(A N B) = (Type an integer or a decimal.) (b) P(A U B) = (Type an integer or a decimal.) (c) P (A' n B') = (Type an integer or a decimal.) (d) P (A'N B) = (Type an integer or a decimal.) (e) P (AN B') = (Type an integer or a decimal.)
Suppose A, B and C are events such that P(A): = 0.46, P(B): = P(BNC) = P(ANC) = 0.16 and P(AnBnC) = 0.06. (a) Are events A and B mutually exclusive? Why? (b) Find P((An BNC)) (c) Find P((AUBUC)) 0.51, P(C) = 0.41, P(An B) =
3. The following is called the Bonferroni's inequality: For events A and B, we have that: P(ANB) ≥ P(A) + P(B) – 1. - a. Prove the Bonferroni inequality. b. Let A and B be events with probabilities P(A) Show that ≤P(AΜB) ≤ } . 12 = 3 and P(B) = 3.
No. 3

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Mathematics For Machine Technology

Advanced Math

ISBN:

9781337798310

Author:

Peterson, John.

Publisher:

Cengage Learning,

Basic Technical Mathematics

Advanced Math

ISBN:

9780134437705

Author:

Washington

Publisher:

PEARSON

Topology

Advanced Math

ISBN:

9780134689517

Author:

Munkres, James R.

Publisher:

Pearson,

SEE MORE TEXTBOOKS

9. Suppose (An) are independent events satisfying P(An) < 1, for all n. Show 8 P(An) = 1 iff P(An i.o. ) = 1. n=1 Give an example to show that the condition P(An) < 1 cannot be dropped.