# What is Conditional: Definition + 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. ### Understanding Conditional Expectation, Variance, and Precision Matrices

My question relates to subsection 2.2.1 of [this article][1]. This subsection recalls the work of Lindgren, Rue, and Lindström (2011) on Gaussian Markov Random Fields (GMRFs). The subsection starts with a two-dimensional regular lattice where the 4 first-order neighbours of $u_{i,j}$ are...

5. ### I Equivalence Question between when-then statement and if then statement

Dear Everybody, I am working on my homework. I am trying to prove a problem that was written by my professor in an odd way: Prove that when p is true, then q is true. Which proposition statement should I assume? I personally thought that I should assume the first one. But reading my...
6. ### Conditional probability problem

A) P(A and B) = 0.45 * 5/10 B P(Not B) = 1 - ( 0.45 * 5/10) Is it like this?
7. ### Python Pix2pix: Image-to-image translation with a conditional GAN

So I am trying to do this tutorials but I want to use my own dataset. I am having problems "Build an input pipeline with tf.data." My question is about their code: def load_image_train(image_file): input_image, real_image = load(image_file) input_image, real_image =...
8. ### MHB What Is the Probability of Distributing Remaining Trump Cards in Bridge?

North and south have ten trumps between them ( trumps being cards of specified suit). (a) Find the probability that all three remaining trumps are in the same hand. (that is either east or west has no trumps). (b) If it is known that king of trumps is included among the three, what is the...
9. ### I Taking socks out of drawers, conditional probability

Problem: In a dresser there are 3 drawers. In one drawer there are two black socks and one white sock, in the second drawer there are two white socks, and in the third drawer there is a black and white sock. Suppose I chose a drawer randomly ( meaning, in a uniform distribution ) and I took a...

23. ### Coulomb's Law and Conditional Convergent Alternating Harmonic Series

Mary Boas attempts to explain this by pointing out that the situation cannot arise because charges will have to be placed individually, and in an order, and that order would represent the order we sum in. That at any point the unplaced infinite charges would form an infinite divergent series...
24. ### B Are proofs needed for definitions? Conditional probabilities

My probability class has me wondering about pure math questions now. We started with the axioms and are slowly building up the theory. Everything was fine but then a definition of Conditional Probability P[A|B] = \frac{P[AB]}{P} appeared and it's just not sitting right with me. I know that...
25. ### I Conditional distribution of geometric series

Can someone help me on this question? I'm finding a very strange probability distribution. Question: Suppose that x_1 and x_2 are independent with x_1 ~ geometric(p) and x_2 ~ geometric (1-p). That's x_1 has geometric distribution with parameter p and x_2 has geometric distribution with...
26. ### Conditional Probability + Poisson Distribution

Confused and not sure if it is correct, but please do correct my steps. We let event B be that there are at least 3 customers entering in 5 minutes. Hence P(B) = 1- P(X=0)- P(X=1) - P(X=2) = ##1- \dfrac{e^{-5}5^{0}}{0!}-\dfrac{e^{-5}5^{1}}{1!}-\dfrac{e^{-5}5^{2}}{2!} ## = 0.8753... Now we let...

32. ### Is an answer possible - Conditional Probability

I am a noob to this topic so correct me If I made any silly mistake. By plugging in the values I managed to get p(abc)=0.75*0.9*p(c|ab) Here How can I find p(c|ab)? Is this question unsolvable or can I derive it? I also want to know what is meant by p(abc) in literary terms. I also created a...
33. ### MHB Absolute and Conditional Convergence .... Sohrab Proposition 2.3.22 ....

I am reading Houshang H. Sohrab's book: "Basic Real Analysis" (Second Edition). I am focused on Chapter 2: Sequences and Series of Real Numbers ... ... I need help with the proof of Proposition 2.3.22 ... Proposition 2.3.12 reads as follows: Can someone please demonstrate (formally and...
34. ### I A Lottery Game With Conditional Probability?

Question: "In a lottery game each player tries to guess right 6 numbers designated in advance by choosing randomly from among numbers from 1 to 20. Given that one player guessed right 5 numbers out of 6 that he/she picked, what is the probability of guessing right the 6 numbers?" The problem...
35. ### Finding conditional and joint probabilities from a table of data

Let, alpha <- c(1, 1) / 2 mat <- matrix(c(1 / 2, 0, 1 / 2, 1), nrow = 2, ncol = 2) chainSim <- function(alpha, mat, n) { out <- numeric(n) out[1] <- sample(1:2, 1, prob = alpha) for(i in 2:n) out[i] <- sample(1:2, 1, prob = mat[out[i - 1], ])...
36. ### How do I derive this expression for conditional probability?

##P(T=1|W=w)=\frac{P(\{T=1\}\cap\{W=w\})}{P(W=w)}=\frac{\binom {n-2} {w-1} p^{w-1}(1-p)^{(n-2)-(w-1)}}{\binom n w p^w (1-p)^{n-w}}=\frac{(n-2)!}{(w-1)!(n-w-1)!}\frac{w!(n-w)!}{n!}\frac{1}{p(1-p)}=\frac{w(n-w)}{n(n-1)}(p(1-p))^{-1}##. I cannot seem to get the terms with ##p## out of my expression.
37. ### MHB Calculating Conditional Probability of Male/Female Customers Buying Books A-D

There are 4 books being sold in the bookshop : A, B, C, D. We know that 20% of the male customers buy book A at least once a week, 55% buy book B at least once a week, 25% buy book C at least once a week and 15% buy book D at least once in a month. We also know that 32% of the female customers...
38. ### Conditional Probability of a continuous joint distribution function

For 1) I found two ways but I get difference results. The first way is I use P(A|B) = P(A and B)/P(B). I get P(X<1|Y<1)=(∫_0^1▒∫_0^1▒〖3/4 (2-x-y)dydx〗)/(∫_0^1▒∫_0^1▒〖3/4 (2-x-y)dydx〗+∫_1^2▒∫_0^(2-x)▒〖3/4 (2-x-y)dydx〗)=6/7 The 2nd method is I use is f(x│y)=f(x,y)/(f_X (x)...
39. ### Insights What is the relevance of Assembler programming in modern technology?

Greg Bernhardt submitted a new blog post AVX-512 Assembly Programming: Opmask Registers for Conditional Arithmetic Conclusion Continue reading the Original Blog Post.
40. ### Insights Are There Libraries for AVX-512 Opmask Registers?

Greg Bernhardt submitted a new blog post AVX-512 Assembly Programming: Opmask Registers for Conditional Arithmetic Continue reading the Original Blog Post.
41. ### Conditional Expectations of 2 Variables

Homework Statement Suppose that the number of eggs laid by a certain insect has a Poisson distribution with mean ##\lambda##. The probability that anyone egg hatches is ##p##. Assume that the eggs hatch independently of one another. Find the expected value of ##Y##, the total number of eggs...
42. ### 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...
43. ### Conditional Entropy and Kullback–Leibler divergence

Homework Statement To find relation between conditional (Shanon) entropy and KL divergence. Homework Equations Conditional Entropy: H[X | Y] = H[X,Y] - H[Y] KL Divergenece: H[X || Y] = -H[X] - Σx ln(y) The Attempt at a Solution H[p(x,y) || p(x)p(y)] = -H[p(x,y)] + H[p(x)] + H[p(y)]
44. ### MHB Conditional Probability and Venn Diagrams

I am having a hard time with the following exercise: Assume for this problem that the company has 8 Chevrolets and 4 Jeeps, and two cars are selected randomly and given to sales representatives. What is the probability of both cars being Chevrolets, given that both are of the same make? I...
45. ### MHB Help with Math Homework: Conditional Probability - 19/30

Hey! I need help with my Math homework :( The question is the following... There are 5 history courses of interest to Howard, including 3 in the afternoon, and there are 6 psychology courses, including 4 in the afternoon. Howard picks a course by selecting a dept at random, then selecting a...
46. ### Conditional probability reasoning problem

Homework Statement Out of all the products a company makes 2% is damaged. During the routine control of the products, the products are put to a test which discovers the damaged ones in 99% of the cases. In 1% however it approves the damaged item as a working one and vice versa. Find the...
47. ### Basic probability, conditional probability

Homework Statement what is the probability that a component which is still working after 800 hrs, will last for at least 900hrs Homework Equations conditional probability P(E|A) = ( P( E ∩ A) ) / ( P(A) ) The Attempt at a SolutionIm just checking my own understanding if this problem is...
48. ### A Value at Risk, Conditional Value at Risk, expected shortfall

I am working on Value at Risk and expected shortfall/conditional Value at Risk.The formula I have is this: What I do not understand is numerator of the second part. If for example I want to look at an expected shortfall when p=0.01 (ignoring the average and the standard deviation). what value...
49. ### MHB Conditional Probability with 3 Events

I'm currently stuck on a question that involves conditional probability with 3 events. This is a concept that I'm having the most trouble grasping and trying to solve in this subject. I am not sure how to start this problem. The Question: Given that P(A n B) = 0.4, P(A n C) = 0.2, P(B|A)=0.6...
50. ### I Equality in conditional probability

Hi In Dudas Pattern Classification, he Writes that P(x,\theta|D) can always be written as P(x|\theta,D)P(\theta|D) . However, I cannot find any justification for this. So, why are these Equal?