Conditional Definition and 483 Threads

In probability theory and statistics, given two jointly distributed random variables



X


{\displaystyle X}
and



Y


{\displaystyle Y}
, the conditional probability distribution of Y given X is the probability distribution of



Y


{\displaystyle Y}
when



X


{\displaystyle X}
is known to be a particular value; in some cases the conditional probabilities may be expressed as functions containing the unspecified value



x


{\displaystyle x}
of



X


{\displaystyle X}
as a parameter. When both



X


{\displaystyle X}
and



Y


{\displaystyle Y}
are categorical variables, a conditional probability table is typically used to represent the conditional probability. The conditional distribution contrasts with the marginal distribution of a random variable, which is its distribution without reference to the value of the other variable.
If the conditional distribution of



Y


{\displaystyle Y}
given



X


{\displaystyle X}
is a continuous distribution, then its probability density function is known as the conditional density function. The properties of a conditional distribution, such as the moments, are often referred to by corresponding names such as the conditional mean and conditional variance.
More generally, one can refer to the conditional distribution of a subset of a set of more than two variables; this conditional distribution is contingent on the values of all the remaining variables, and if more than one variable is included in the subset then this conditional distribution is the conditional joint distribution of the included variables.

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  1. M

    Conditional Binomial Distribution

    Hi guys, I can't get my head around this, if anyone could help that would be great. "A robotic assembly line contains 20 stations. Suppose that the probability that each individual station will fail is 0.3 and that the stations fail indepen- dently of each other. Given that at least one...
  2. L

    Measure theoretic definition of conditional expecation

    I've been looking at the measure theoretic definition of a conditional expectation and it doesn't make too much sense to me. Consider the definition given here: https://en.wikipedia.org/wiki/Conditional_expectation#Formal_definition It says for a probability space (\Omega,\mathcal{A},P), and...
  3. 3

    Conditional Probability on Intermediate Event

    I have seen in class the following formula used: P(A | C) = \sum_{B} P(A | B \cap C)*P(B | C) I don't understand how this formula works? Can anyone help me understand how it can be derived and how I can understand it intuitively? Can a venn diagram be drawn to illustrate this formula?
  4. I

    Calculating Joint Conditional Probability with Independent Variables

    Homework Statement I have access to P(x|A) and P(y|A), P(x), P(y) and P(A), in addition to the knowledge that x and y are independent variables. I am interested in finding P(A|x,y). The Attempt at a Solution I think that P(A|x,y) = P(x,y|A) * P(A) / P(x,y) = P(x,y|A) * P(A) /...
  5. C

    Exponential Random Variables and Conditional Probability Problem

    Homework Statement A submarine has three navigational devices but can remain at sea if at least two are working. Suppose that the failure times are exponential with means 1 year, 1.5 years, and 3 years. What is the average length of time the boat can remain at sea?Homework Equations Density...
  6. T

    Using ratio test to test conditional convergence?

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  7. T

    Decompostion of conditional probabilities

    So If B=B1UB2U...UBn would Pr(A|B)=Pr(A|B1)Pr(B1)+Pr(A|B2)Pr(B2)+...+Pr(A|Bn)Pr(Bn)? I haven't found a formula for this but it makes intuitive sense.
  8. J

    Conditional probability & r balls randomly distributed in n cells

    Conditional probability & "r balls randomly distributed in n cells" Homework Statement I'm posting this in hope that someone can give me a correct interpretation of the following problem (problem V.8 of Feller's Introduction to probability theory and its applications VOL I): 8. Seven balls...
  9. T

    Selecting from an Urn. Conditional probability

    Homework Statement A box contains 4 red balls and 6 white balls. A sample size of 3 is drawn without replacement from the box. What is the probability of obtaining 1 red ball and 2 white balls given that at least 2 of the balls in the sample are white? Homework Equations The...
  10. K

    Terrible conditional probability problems

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  11. T

    Conditional Probability without Bayes rule

    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...
  12. K

    Conditional probability problem

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  13. G

    What Is the Probability an Email Quarantined as Spam Is Actually Spam?

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  14. L

    Absolute and conditional convergence of series (1 + x/n)^n^2

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  15. P

    Computing partial (conditional) correlation

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  16. I

    Conditional Expectation Problem

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  17. S

    Conditional Formatting Issue in Excel

    Hi everyone. I have never worked in-depth with Excel and I am trying to make my life a bit simpler doing some data cleaning using the 'conditional formatting' option. My scenario is the following: I have two columns of data, column A and column B. I would like to take each entry (a string...
  18. S

    Conditional expectation, Lebesgue measure

    Homework Statement Let Ω = [0,1] with the σ-field of Borel sets and let P be the Lebesgue measure on [0,1]. Find E(X|Y) if: Homework Equations X(w)=5w^2 Y(w)= \left\{ \begin{array}{ll} 4 & \mbox{if $w \in [0,\frac{1}{4}]$} \\ 2 & \mbox{if $w \in (\frac{1}{4},1]$} \\ \end{array}...
  19. J

    MHB Showing Conditional Independence Does Not Imply Independence

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  20. D

    Are the events A1 and A2 conditionally independent, given F2?

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  21. L

    Calculating Conditional Probability for Steroid Use at the Olympics

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  22. L

    Conditional Probability problem

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  23. L

    Conditional Probability of computer password

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  24. K

    [Statistics] Conditional Probability questions?

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  25. A

    MHB Conditional Independence and Independence question

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  26. B

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  27. I

    Help with conditional probability

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  28. R

    MHB What is the probability that a tested detail was faulty?

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  29. S

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  31. D

    Conditional and absolute convergence (of series)

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  32. M

    Kept getting the wrong answer? binomial conditional probability

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  33. T

    Conditional Probabilities problem

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  34. T

    Alternating Series Tests: Understanding Conditional & Absolute Convergence

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  35. D

    Conditional PDF and Expectation: How to Calculate Them?

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  36. P

    Conditional Probability: probability of having a girl.

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  37. N

    Definition of conditional probability density

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  38. A

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  39. I

    Formula for entropy conditional on >1 variables?

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  40. K

    Are Random Variables X and Y Related If Their Conditional Probabilities Change?

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  41. K

    Need help with a conditional variance proof.

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  42. O

    Conditional expectations question

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  43. Z

    Conditional probability question with set theory things

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  44. S

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  45. X

    Compute the conditional probability

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  46. H

    A conditional probability question on picking out chips from a bowl.

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  47. H

    Conditional probability drawing two balls from an urn.

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  48. B

    What Is the Probability Juliet Replies on Tuesday If She Hasn't on Monday?

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  49. C

    Is E(A+B|C) Equal to E(A|C) + E(B|C)?

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  50. G

    Conditional statement that will prevent users from imputing

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