answer no. 3 only II. Do what is indicated in order to answer the following problems, use only blue or black pen. Do asneatly as you can.1. Suppose that P₁ and P2 are probabilities on (02, E) and that 0 s co s 1. Prove thatP(A) = ∞ P₁(A) + ∞oP₂(A) is also a probability.2. Five red books, six green books, and four blue books are to be arranged on a shelf. What is theprobability that at least 3 green books all stand together?3. Let = {1,2,3,4,} and C= {{1,2,3}, {4}}. Derive the sigma-algebra generated by C, i.e. that smallestsigma-algebra that contains C.4. A person wins a contest in which he gets a free trip from San Diego (SD) to New York (NY) via LosAngeles (LA) and Chicago (CH). He has a choice of two buses from SD to LA. Once in LA, he has achoice of 3 plane flights to CH, and upon arrival in CH he has a choice of 2 trains to NY. Let & bethe event that he catches bus i(i=1,2), P, the event that he catches plane /(1,2,3), and T. theevent that he catches train /(-1,2). Express the following in terms of B, P, T: (a) the event thatthe person gets to NY; and (b) the event that the person does not get to NY.5. Discuss the following:a) probability using axiomatic approachb) o-algebrac) mutually exclusive and independent eventsd) pairwise independence and independence eventsf) conditional probabilitye) subjective probability

Given: Ω=1,2,3,4 C=1,2,3,{4}Find:Derive the sigma-algebra generated by C.

Answered: 3. Let = {1,2,3,4,) and C= {{1,2,3},…

3. Let = {1,2,3,4,) and C= {{1,2,3}, {4}}. Derive the sigma-algebra generated by C, i.e. that smallest sigma-algebra that contains C.

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter14: Counting And Probability

Section14.2: Probability

Problem 3E: The conditional probability of E given that F occurs is P(EF)=___________. So in rolling a die the...

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Question

answer no. 3 only

II. Do what is indicated in order to answer the following problems, use only blue or black pen. Do as
neatly as you can.
1. Suppose that P₁ and P2 are probabilities on (02, E) and that 0 s co s 1. Prove that
P(A) = ∞ P₁(A) + ∞oP₂(A) is also a probability.
2. Five red books, six green books, and four blue books are to be arranged on a shelf. What is the
probability that at least 3 green books all stand together?
3. Let = {1,2,3,4,} and C= {{1,2,3}, {4}}. Derive the sigma-algebra generated by C, i.e. that smallest
sigma-algebra that contains C.
4. A person wins a contest in which he gets a free trip from San Diego (SD) to New York (NY) via Los
Angeles (LA) and Chicago (CH). He has a choice of two buses from SD to LA. Once in LA, he has a
choice of 3 plane flights to CH, and upon arrival in CH he has a choice of 2 trains to NY. Let & be
the event that he catches bus i(i=1,2), P, the event that he catches plane /(1,2,3), and T. the
event that he catches train /(-1,2). Express the following in terms of B, P, T: (a) the event that
the person gets to NY; and (b) the event that the person does not get to NY.
5. Discuss the following:
a) probability using axiomatic approach
b) o-algebra
c) mutually exclusive and independent events
d) pairwise independence and independence events
f) conditional probability
e) subjective probability

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