Show that two events A and B are independent if and only if P (A B)

Question:

Show that two events A and B are independent if and only if P (A ∩ B) = P (A) P (B) when at least one of P (A) or P (B) is not zero.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Mathematical Statistics With Applications In R

ISBN: 9780124171138

2nd Edition

Authors: Chris P. Tsokos, K.M. Ramachandran

See More Books

Question Posted: Nov 23, 2015 03:37 AM

See More Questions

Suppose two events A and B are independent. (a) Is it true that A is independent of B? If yes, give a convincing proof, otherwise, give a counterexample. (b) Is it true that is independent of B? If...
Two events, A and B, are independent, with P(A) = .3 and P(B) = .1. a. Are A and B mutually exclusive? Why? b. Find P(A\B) and P(B\A). c. Find P(A B).
If two events A and B are such that Pr(A) is not zero and Pr(B) is not zero, what combinations of independent (I ), not independent (NI ), mutually exclusive (M), and not mutually exclusive (NM) are...
Determine the range of the 2x function y = 3 sec 3
The data set below shows a sample of salaries for 39 engineers employed by the Solnar Company along with each engineer's years of experience. (a) Construct a scatter plot using Salary as the response...
A company has developed a promising new product and examines the following three alternatives of manufacturing. Alternative No. 1 is to buy a semi-automatic machine with an initial cost of 130,000,...
Why do welfare programs create work disincentives?
Harrison Wolfe operates a residential landscaping business in an affluent suburb of Atlanta. In an effort to provide quality service, he has concentrated solely on the design and installation of...
A one cubic foot sample of a borrow-source clay weighed 88 lbs. If the specific gravity of solids was measured as 2.70, and the clay was found to be 10 percent saturated, determine the water content...
Rusty Spears, CEO of Rusty's Renovations, a custom building and repair company, is preparing documentation for a line of credit request from his commercial banker. Among the required documents is a...
If A and B are independent, show that so are (i) Ac and B, (ii) A and Bc, and (iii) Ac and Bc.
A card is elected at random from an ordinary deck of 52 playing cards. If E is the event that the selected card is an ace and F is the event that it is a spade, show that E and F are independent...
Why do people make inadvertent mistakes? How does poka-yoke help prevent such mistakes?
What are some issues that could come up during the research and development stage of a new product that would be a reason to delay it's launch or give up on the idea completely?
Match the following terms to the correct definitions. Drag and drop application. Fraudulent financial reporting Fraudulent financial reporting drop zone empty. Misappropriation of assets...
Find the number of subsets of set S. S = {1, 2, 3, ..., 9}
The sale of land that was held for business-use purposes results in what type of gain or loss?
What are the Compliance-Based Codes of Ethics and Value-Based Codes of Ethics? Why are they important in International Ventures? Describe why responsible sourcing is included in many organizational...
Write in intercept form the equation of the line satisfying the given conditions. Then find the x- and y-intercepts of the line. Slope -2, passing through (3,-1)
Shreemaya Hotel in !adore was facing a problem of low demand for its rooms due to off season. The Managing Director (MD) of the hotel, Mrs. Sakina was very worried. She called upon the Marketing...
In a manufacturing operation, a part is produced by machining, polishing, and painting. If there are three machine tools, four polishing tools, and three painting tools, how many different routings...
New designs for a wastewater treatment tank have proposed three possible shapes, four possible sizes, three locations for input valves, and four locations for output valves. How many different...
A manufacturing process consists of 10 operations that can be completed in any order. How many different production sequences are possible?
Martin Company applies manufacturing overhead based on direct labor hours. Information concerning manufacturing overhead and labor for the year is as follows: Actual manufacturing overhead Estimated...
$ 719,000 280,000 439,000 150,400 Joyner Company's income statement for Year 2 follows: Sales Cost of goods sold Gross margin Selling and administrative expenses Net operating income Nonoperating...
FIFO and LIFO costs under perpetual inventory system The following units of an item were available for sale during the year: Beginning inventory 22 units at $44 Sale 18 units at $62 First purchase 18...

Show that two events A and B are independent if and only if P (A B)

Question:

Step by Step Answer:

If A and B are independent th...View the full answer

Mathematical Statistics With Applications In R

Students also viewed these Statistics questions