Bayes rule Definition and 15 Threads

I got (a) and (b) but I'm still working on (c). The solutions can be found here for your reference: https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-041sc-probabilistic-systems-analysis-and-applied-probability-fall-2013/unit-ii/lecture-9/MIT6_041SCF13_assn05_sol.pdf. But...

Hello! I'm sitting with a problem that is causing me some troubles.. First part is using Bayes formula. We have 3 companies that produce some apparatus. Each company has some defective percentage. Company Produced (%) Defective (%) A 45 3 B 25 6 C 30 5 1) Suppose we pick up a...

Hello! I am trying to get to grips with the Bayes' formula by developing an intuition about the formula itself, and on how to use it, and how to interpret. Please, take a problem, and my questions written within them - I will highlight my questions and will post them as I add the information...

Hi, I'm not sure whether my understanding of this question is correct: An app predicts rain tomorrow. Recently, it has rained only 73 days each year. When it actually rains, the app correctly forecasts rain 70% of the time. When it does not rain, it incorrectly forecasts rain 30% of the time...

Homework Statement Suppose you’re on a game show and you’re given the choice of three doors. Behind one is a car, behind the others are goats. You pick a door, say number 1, and the host, who knows what’s behind the doors, opens another door, say number 3 which has a goat. He says to you, “Do...

As stated in my subject line, I know that P(A|B) = P(A) and P(B|A) = P(B), i.e. A and B are separable as P(A,B) = P(A) P(B). I strongly suspect that this holds with a conditional added, but I can't find a way to formally prove it... can anyone prove this in a couple of lines via Bayes' rules...

Hi, I am teaching a machine learning course and the students have very poor knowledge about conditional probability, Bayes rule etc. Most students have done their undergraduates years ago and I guess their educational background has not been that good. Last lecture was on Naive Bayes...

Suppose X and Y are independent Poisson random variables with respective parameters λ and 2λ. Find E[Y − X|X + Y = 10]3: I had my Applied Probability Midterm today and this question was on it. The class is only 14 people and no one I talked to did it correctly. The prof sent out an e-mail saying...

I try to understand the following equation but I can not. I have basic knowledge about Bayes rule and joint probability. How can we produce this result? I would appreciate any help. p(R|q,x)/p(NR|q,x)=[p(R|q) / p(NR|q) ] * [p(x|R,q) / p(x|NR,q)]

Is the rule: P(AB I) = P(BA I) (which is used to derive Bayes rule) an axiom for probability? And if so, do you guys find it intuitive that it should hold. For instance consider a box with green and red beads. Do you think it is strictly obvious that the probability of getting red-green is...

Homework Statement I am just wanting to get a good starting point... not an answer to the question. Question: A desk contains three drawers. Drawer 1 has two gold coins. Drawer 3 has one gold coin and one silver coin. Drawer 3 has two silver coins. I randomly choose a drawer and then randomly...

Say I want to find Pr(A|B). Usually I would just use bayes rule, but some textbooks just assume that A|B works and then just multiply it by P(B). For example in my book, Pr(X>2000)=.4. X and Y are unif distributed from 1000 to 5000. They are independent. Find Pr(X+Y>8000|X>2000). Well they just...

Homework Statement Event B is cow has BSE Event T is the test for BSE is positive P(B) = 1.3*10^-5 P(T|B) = .70 probability that the test is positive, given that the cow has BSE P(T|Bcc) = .10 probability that the test is positive given that the cow does not have BSE Find P(B|T) and...

Hi I am asking, if I am trying to make inference using Bayes rule based on a prior probability that is a random variable by itself; is it sufficient to use the expected value of such probability or there are other details. Thanks in advance.