1. Definition
If E and F are two events associated with the same sample space of a random experment, the conditional probability of the event E given that F has occurred, i.e. P(E|F) is given by
P(E|F) = (E∩F)/P(F) (P≠0)
2. Properties of conditional probability
Let E and F be events of...
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...
Hello.
I am reading an online stats book, and there is the following question, which I solved incorrectly, and I think I understand what is my mistake, but I will be grateful for your explanation, if I have incorrectly detected the logic behind my mistake. I am weak at math (trying to improve it...
Hi,
I was having some trouble doing some bayesian probability problems and was wondering if I could get any help. I think I was able to get the first two but am confused on the last. If someone could please check my work to make sure I am correct and help me on the last question that would be...
I scored in the 88th percentile in a certain personality trait and am trying to figure out the probability of that given that I'm male. I'm trying the likelihood that I would land in the 88th percentile given that I'm male.
Definitions: T = trait, M = males, F = female.
Given:
P(T|M) = 0.3...
Su, Francis, et. al. have a short description of the paradox here: https://www.math.hmc.edu/funfacts/ffiles/20001.6-8.shtml
I used that link because it concisely sets forth the paradox both in the basic setting but also given the version where the two envelopes contain ( \,\$2^k, \$2^{k+1}) \...
Homework Statement
The probability density function for a random vector ##(X,Y)## is ##f(x,y) = 3x##, when ##0 < y< x < 1##. Calculate the conditional probability
P(X> \frac{1}{2} | Y > \frac{1}{3})
Homework Equations
Conditional probability:
\begin{equation}
P(A | B) = \frac{P(A \cap...
I've found this video about conditional probability:
All steps look correctly, but the result does not make any sense.
I'm ok with the part about frogs, but not so with the boy/girl computation.
To sum it up:
1) I have two children and at least one of them is a boy. What is a probability I...
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...
So I was checking the How to self-study math thread and saw that someone suggested that It would be helpfull to create this kind of thread.
And because we are writting a test on thursday on Probability I though it would be nice to find out which parts I still need to double-check.
So these...
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...
Homework Statement
A company has been running a television advertisement for one of its new products. A survey was conducted. Based on its results, it was concluded that an individual buys the product with probability...
P(A/B) is defined to be P(A∩B)/P(B)
Why is this true?
When A and B are dependent events, I can understand why this is correct. It is clear when you see the venn diagram.
But for independent events, why is the formula correct? Any intuition or formal proof?
Basically I am wondering how you deal with a conditional cdf and turning that into a conditional pdf when the random variables are independent. I know that f(X|Y) =f(X)f(Y)/f(Y)=f(X)
I tried to derive this in a nice attached laTex document but it does not seem right to me.
Note(this is for a...
Homework Statement
Let X and Y be independent Bernoulli RV's with parameter p. Find,
\mathbb{E}[X\vert 1_{\{X+Y=0\}}] and \mathbb{E}[Y\vert 1_{\{X+Y=0\}}]
Homework Equations
The Attempt at a Solution
I'm trying to show that,
\mathbb{E}[X+Y\vert 1_{\{X+Y=0\}}] = 0
by,
\begin{align*}...
Homework Statement
Let f(x1, x2, x3) = e-(x1+x2+x3), 0<x1,2,3<infinity, zero elsewhere be a joint pdf of X1, X2, X3. The variables are all independent to each other
Compute P(X1< X2< X3|X3<1 )
Homework Equations
P(X1< X2< X3|X3<1 )
The Attempt at a Solution
P(X1< X2< X3|X3<1 )=P(X1< X2< X3<1...