Topics about conditional probability - 16 Discussions, Page 1

  1. CaptainX

    B Conditional Probability

    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...
  2. Vital

    I Bayes' formula

    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...
  3. Vital

    I Conditional probability choosing from the objects

    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...
  4. R

    Bayesian Probability Distributions

    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...
  5. J

    B Probability and Percentiles

    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...
  6. A

    I Question: Proposed Solution to Two Envelope Paradox

    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}) \...
  7. TheSodesa

    Conditional probability for a random vector

    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...
  8. SlowThinker

    B Boy/girl riddle (conditional probability)

    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...
  9. N

    Is P(A,B|C) = P(A|C) P(B|C), if P(A,B) = P(A)P(B)?

    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...
  10. Matejxx1

    Please ask me questions to challenge my knowledge

    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...
  11. W

    Prob/Stats Easy text on conditional probability and Bayes theory

    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...
  12. C

    Probability of Randomly Selective Event, Conditional Probability

    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...
  13. A

    Conditional Probability Formula

    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?
  14. J

    Conditional Probability

    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...
  15. I

    Conditional expectation on an indicator

    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*}...
  16. J

    How to integrate this one P(x1<x2<x3<1)

    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...
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