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
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
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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answer no. 5 only
Transcribed Image Text: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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