Questions tagged [conditional-probability]

Question 1

Let $(\Omega, \mathcal{A}, \mathbb{P})$ be a probability space and $X:(\Omega, \mathcal{A})\rightarrow (\mathcal{X}, \mathcal{F})$ and $Y:(\Omega, \mathcal{A})\rightarrow (\mathcal{Y}, \mathcal{G})$ ...

Question 2

There are perhaps some related questions on this site already (I can think of this question, this or this), but I want to be more concrete here. In the linked questions, and e.g. in Dudley's book (...

Question 3

The problem is the following: We roll a fair die until we get 6. What is the expected number of rolls conditioned on the event that all rolls only gave even numbers ($2,4$)? This problem can be ...

Question 4

I have a great confusion with the definition of a regular conditional probability versus a section on the same subject I think in Le Gall's book Measure theory, probability and stochastic processes. ...

Question 5

I was just solving problems on conditional probabilities. When I was taught this concept, most of the conditions were given for specific value. But then I saw an example where the condition was that X ...

Question 6

I am working on a fairly simple problem: "When rolling a fair dice 12 times, what is the probability of getting 2 of each number" My immediate instinct was to calculate as follows, in this ...

Question 7

I am working on the following exercise. Let $$X_1 \sim \mathrm{Exp}\left(\tfrac12\right), \qquad X_2 \sim \mathrm{Exp}\left(\tfrac12\right),$$ independent. Define $$Y_1 = X_1 + 2X_2, \qquad Y_2 = 2X_1 ...

Question 8

Let $X$ and $Y$ be two random variables. Then, define $X\mid\{Y = y\}$ as the random variable that takes outcomes from a subset of the sample space defined by the event $\{Y=y\}$. Assume further that $...

Question 9

Let $(\Omega,\mathcal F, P)$ be a probability space and $Z:\Omega\to\mathbb R$ be a random variable. $Y: (\Omega,\mathcal F)\to (\Lambda,\mathcal G)$ is a measurable map between these two measurable ...

Question 10

So given a probability space $(\Omega, \mathcal{A}, P)$ and sub-$\sigma$-algebra $\mathcal{G}\subseteq\mathcal{A}$, consider the conditional probability $P(A|\mathcal{G})$ for any $A\in\mathcal{A}$. ...

Question 11

I conduct $X \sim \text{Poisson}(\lambda = 1)$ experiments. Each experiment is IID, with probability $p$ of outcome $\bf A$ and $q = 1-p$ of $\bf B$. Let $A, B$ be the total number of experiments with ...

Question 12

This problem and solution are directly transcribed from a study guide. A bag contains n blue and m red marbles. You randomly pick a marble from the bag, write down its color, and then put the marble ...

Question 13

Let $X$ be a discrete random variable and $Y$ be a continuous random variable. I can't seem to come up with an explanation as to why $X|Y$ is always discrete. How do I see this intuitively?

Question 14

All, In my lecture, I read the following statement. We are working on a probability space $(\Omega, \mathcal{F}, \mathbb{P})$. Let $\mathcal{F'}$ be a sigma-field generated by, say, two random ...

Question 15

The tower property (law of total expectation) states that for any $σ$-subalgebras $G_1 ⊆ G_2$ $$ \text{(I)} \qquad E[X∣G_1] = E[E[X∣G_2] ∣ G_1] \qquad\text{a.s.} $$ In particular, for an integrable ...

Stack Exchange Network

Questions tagged [conditional-probability]

Joint distribution and coupling of marginal with conditional distribution

A concrete example of why we need regular conditional probability

Expected number of die rolls until we hit $6$ conditioned on just seeing even numbers

Regular conditional probability being a measure almost everywhere; Le Gall

Conditioning that a random variable is another random variable

Sequences of Independent Probabilities Intuition

Conditional probability for linear combinations of independent exponentials

Definition of conditional random variables [duplicate]

Prove a formula on conditional probability: $E(g(X,Y)| Y=y)= E(g(X,y)|Y=y)$.

Conditional probabilities can fail to be probability measures. Can they also fail to be a measure?

The number of positive outcomes is independent of the number of negative outcomes (under Poisson)

In this problem, why is the probability P(S) equal to P(B)P(B) + P(R)P(R) according to the law of total probability?

Conditioning a discrete random variable on a continuous random variable [closed]

Conditional expectation for "nested" sigma-fields

Tower Property implications on the conditional distribution

Hot Network Questions