New posts in probability

Coin probability

probability bayes-theorem

Same distribution with different probability density function

probability probability-distributions moment-generating-functions

Let $X$ be a random variable with Cauchy distribution, compute the density function of $Y=\frac{1}{1+X^2}$

probability probability-theory probability-distributions density-function

Intuition for Conditional Expectation

real-analysis probability probability-theory measure-theory conditional-expectation

What constitutes an outcome in probability?

Exercise Problem 43, Chapter 4, Intro to Probability, Blitzstein and Hwang

probability solution-verification expected-value self-learning

What can I do with measure theory that I can't with probability and statistics

probability measure-theory statistics probability-theory

What are efficient data structures and algorithms for simulating loaded dice?

algorithm language-agnostic data-structures random probability

Make $2$ cubes out of $1729$ unit cubes, expected number of times you have to paint

probability combinatorics algebra-precalculus contest-math expected-value

The Probability $P_{[m]}$ that exactly $m$ among the $N$ events $A_1,\dots,A_N$ occur simultaneously

probability combinatorics probability-theory

If $X,Y$ are independent $\chi ^2$ with $m$ and $n$ degrees of freedom, then $\frac{X}{X+Y} \sim\beta(m/2, n/2)$

probability probability-distributions density-function

Proof that if $Z$ is standard normal, then $Z^2$ is distributed Chi-Square (1).

probability statistics normal-distribution moment-generating-functions

No two identical ranks together in a standard deck of cards

probability combinatorics

What is the probability that a natural number is a sum of two squares?

probability number-theory

Show that a distribution function is dominated

probability measure-theory statistics probability-distributions

Finding the covariance matrix of a multivariate gaussian

probability statistics normal-distribution covariance gaussian

Verify whether $\mathbb{E}\int_{0}^{\infty}\frac{|B_t|}{(1+B_t^2)^2}\mathrm{d}t < \infty$

probability probability-theory expected-value brownian-motion

Let $Y_n,X_n$ be a sequence of r.v. Does $\sup_z \Big|P(Y_n<z\ |\ X_n) - \Phi(z)\Big|\rightarrow_p0 \implies \{Y_n|X_n=x_n\}\xrightarrow[]{d}N(0,1)?$

real-analysis probability probability-theory statistics probability-distributions

The mean distribution versus distribution over mean of distribution over distributions?

probability probability-distributions bayesian

Prove that if events A and B are independent, then the complement events of A and B are also independent.