(a) Let P(B1 N B2) > 0, and A1 U A2 C B1 N B2. Then show that P(A||B1) .P (A2\B2) = P (A||B2) .P (A2|B1). %3D (b) Let A and B1 be independent; similarly, let A and B2 be independent. Show that in this case, A and B1 U B2 are independent if and only if A and B1 N B2 are independent. (c) Given P(A) = 0.42, P(B) = 0.25, and P (An B) = 0.17, find (i) P(AU B); (ii) P(An Bº); (iii) P(Aºn B°); (iv) P(A°|B®).

(a) Let P(B1 N B2) > 0, and A1 U A2 C B1 N B2. Then show that P(A||B1) .P (A2\B2) = P (A||B2) .P (A2|B1). %3D (b) Let A and B1 be independent; similarly, let A and B2 be independent. Show that in this case, A and B1 U B2 are independent if and only if A and B1 N B2 are independent. (c) Given P(A) = 0.42, P(B) = 0.25, and P (An B) = 0.17, find (i) P(AU B); (ii) P(An Bº); (iii) P(Aºn B°); (iv) P(A°|B®).

Name: (a) Let P(B1 N B2) > 0, and A1 U A2 C B1 N B2. Then show thatP(A||B1)
Uploaded: 2024-03-05T11:52:21.000Z
Channel: Bartleby
Description: (a) Let P(B1 N B2) > 0, and A1 U A2 C B1 N B2. Then show thatP(A||B1) .P (A2\B2) = P (A||B2) .P (A2|B1).%3D(b) Let A and B1 be independent; similarly, let A and B2 be independent. Show that in thiscase, A and B1 U B2 are independent if and only if A

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 28EQ

See similar textbooks

Similar questions

s1) a)X ∼ exp (λ). Under the condition {X> 3} fX | {X> 3} (x | X> 3) =? and E [X | X> 3] =?
If A is satisfied as A2 - 6A + 5In = 0, what is A-1
When an automobile is stopped by a roving safety patrol, each tire is checked for tire wear, and each headlight is checked to see whether it is properly aimed. Let X denote the number of headlights that need adjustment, and let Y denote the number of defective tires. (a) If X and Y are independent with pX(0) = 0.5, pX(1) = 0.3, pX(2) = 0.2, and pY(0) = 0.6, pY(1) = 0.1, pY(2) = pY(3) = 0.05, pY(4) = 0.2, display the joint pmf of (X, Y) in a joint probability table. y p(x, y) 0 1 2 3 4 x 0 1 2 (b) Compute P(X ≤ 1 and Y ≤ 1) from the joint probability table.P(X ≤ 1 and Y ≤ 1) = (c) What is P(X + Y = 0) (the probability of no violations)?P(X + Y = 0) =
4. Show that if ax2 + bx + c = 0 for all x, then a = b = c =0
Your major online bookstore is in direct competition with Amazon.com, BN.com, and BooksAMillion.com. Your company's daily revenue in dollars is given by R(x, y, z) = 10,000 − 0.01x − 0.02y − 0.01z + 0.00001yz, where x, y, and z are the online daily revenues of Amazon.com, BN.com, and BooksAMillion.com respectively. (a) If, on a certain day, Amazon.com shows revenue of $10,000, while BN.com and BooksAMillion.com each show $5,000, what does the model predict for your company's revenue that day?$ ________(b) If Amazon.com and BN.com each show daily revenue of $5,000, give an equation showing how your daily revenue depends on that of BooksAMillion.com. R(z)________
If f1x2 = 2x3 + Ax2 + 4x - 5 and f122 = 5, what is thevalue of A?
nternet Audience At the end of a certain year, the four companies with the largest number of home Internet users in the United States were Microsoft, Time Warner, Yahoo, and Google, with a combined audience of 284 million users. Taking x to be the Microsoft audience in millions, y the Time Warner audience in millions, z the Yahoo audience in millions, and u the Google audience in millions, it was observed that z − u = 3(x − y) + 22 x + y = 44 + z + u and x − y + z − u = 46. How large was the audience of each of the four companies at the end of that year? MicrosoftTime WarnerYahooGoogle
An agent makes decisions using U(ct) = {[ct−χc(t−1)]^(1−γ)} /(1−γ) . Answer the following: (a) Suppose χ = 0. Derive an expression for the coefficient of relative risk aversion RR(ct)? (b) Suppose 0 < χ ≤ 1. Derive an expression for the coefficient of relative risk aversion RR(ct) (c) Suppose 0 < χ ≤ 1. How does this utility function help address the equity premium puzzle? (d) Suppose χ = .4, γ = 0.5, ct = 105, and ct−1 = 100, what is the coefficient of relative risk aversion? (e) Suppose 0 < χ ≤ 1. Suppose the agent is confronted with a mean preserving spread where ˜RB is riskier than ˜RA and where E[˜RA] = E[˜RB] and ˜RA SSD ˜RB. Derive the restriction for the value of γ where the agent saves more today under ˜RB than ˜RA. (f) Suppose χ = .4, γ = 0.5, ct = 105, and ct−1 = 100, what value must γ be greater than for the agent to save more today under the mean preserving spread
When random samples are drawn so that the selection of a case for one sample has no effect on the selection of cases for another sample, the samples are A. Dependent B. Independent C. Simple D. Systemo
Maximize B=4xy2, where x and y are positive numbers such that x+y2=1.
for a is it possible tomake u=y^2+x^2?
Let A = {m ∈ Z|m = 4k + 8} where k ∈ Z, and let B = {n ∈ Z|n = 2r + 2} where r ∈ Z. Show |A| = |B|.