Question: 42. Let A1, A2, A3, . . . be a sequence of events of a sample space. Prove that P [ n=1 An

42. Let A1, A2, A3, . . . be a sequence of events of a sample space. Prove that P

 ∞[

n=1 An



≤

∞X n=1 P(An).

This is called Boole’s inequality.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Probability And Stochastic Modeling Questions!

Q:

28. Let A1, A2, A3, ... be a sequence of events of a sample space. Prove that P *+ n=1 An , . n=1 P (An). This is called Booles inequality.

Q:

Change issue 16 in portion 4.2 of your substance, including drawing markers from a compartment of markers with ink and markers without ink. Expect that the case contains 19 markers: 14 that contain...

Q:

BA 1605: Midterm Recap (Due: Feb. 27, 2015) Name _____________________________ 50 Student ID _____________________________ Section 01B 10:00~11:20 am Section 02B 01:00~02:20 pm [Questions 4 ~ 7] The...

Q:

42. Let A1, A2, A3, . . . be a sequence of events of a sample space. Prove that This is called Booles inequality. P(UA) P(An). n=1 n=1

Q:

Please show the step by step answer below(question 5),this is not assignment question. the event b is impossible if and only if for every event A. A = (BnA' ) U ( Ben A ). 4. Cards In an experiment,...

Q:

29. Let A1, A2, A3,... be a sequence of events of an experiment. Prove that P *- n=1 An , 1 . n=1 P (Ac n). Hint: Use Booles inequality, discussed in Exercise 28.

Q:

12 Let (A1, A2, A3, ...) be a sequence of events. Prove that if the series = P(A) converges, then P (UA) = 0. This is called the Borel-Cantelli lemma. It says that if P(A)

Q:

12. Let{A1, A2, A3,...} be a sequence of events. Prove that if the series/ n=1 P (An) converges, then P * ) m=1 ( n=m An , = 0. This is called the Borel-Cantelli lemma. It says that if / n=1 P (An)

Q:

Convex geometry 0.1 Dehn-Sommerville relations In this section we will talk about convex polytopes. One possible denition of a convex polytope uses the notion of a half-space: A closed half-space in...

Q:

1. A player throws a fair die and simultaneously flips a fair coin. If the coin lands heads, then she wins twice, and if tails, then one-half of the value that appears on the die. Determine her...

Q:

Show that in a group of 10 people (where any two people are either friends or enemies), there are either three mutual friends or four mutual enemies, and there are either three mutual enemies or four...

Q:

Alison worked as an administrative assistant for one and one-half years. When she left this position, she was one month shy of her 21st birthday. Upon leaving her job, Alison discovered she had no...

Q:

i What does the contrast in 'The sand of his village was replaced with granite, mud with cement, fish with scraps of rubbery mutton' suggest about the difference between Salaamat's village and the...

Q:

Draw all constitutional isomers with molecular formula C 4 H 11 N, and provide a name for each isomer.