Linked Questions

0 votes
0 answers

Probability RV is min among several iid RVs [duplicate]

This question is inspired by this programming question. Suppose I have 3 RVs which are independent. $$X \sim N(25.5, 2.5)$$ $$Y \sim N(25.2, 3.5)$$ $$Z \sim N(24.9, 1.7)$$ I want to know what is the ...
Dean MacGregor's user avatar
17 votes
3 answers

Which is largest, of a bunch of normally distributed random variables?

I have random variables $X_0,X_1,\dots,X_n$. $X_0$ has a normal distribution with mean $\mu>0$ and variance $1$. The $X_1,\dots,X_n$ rvs are normally distributed with mean $0$ and variance $1$. ...
D.W.'s user avatar
  • 6,528
9 votes
5 answers

$P(X_1 < \min(X_i,\ldots, X_n))$ across different normal random variables

I have a set of mutually independent normal distributions $X_1$ to $X_5$ (with means and standard deviations) which represent finishing times for swimmers over a certain distance. The actual data is ...
Jason's user avatar
  • 113
9 votes
3 answers

What is the probability that random variable $x_1$ is maximum of random vector $X=(x_i)$ from a multivariate normal distribution?

Given a $n$-dimensional multivariate normal distribution $X=(x_i) \sim \mathcal{N}(\mu, \Sigma)$ with mean $\mu$ and covariance matrix $\Sigma$, what is the probability that $\forall j\in {1,\ldots,n}:...
gregor's user avatar
  • 281
6 votes
2 answers

What is a method to calculate precisely $P(Y \geq X, Y\leq Z)$, given three independent random variables $X, Y$, and $Z$

For three independent normally distributed continuous random variables X, Y, and Z (each with its own mean and standard deviation), I need a way to calculate $P(Y \geq X, Y \leq Z)$ I know that I ...
Abey's user avatar
  • 63
21 votes
2 answers

How can we bound the probability that a random variable is maximal?

$\newcommand{\P}{\mathbb{P}}$Suppose we have $N$ independent random variables $X_1$, $\ldots$, $X_n$ with finite means $\mu_1 \leq \ldots \leq \mu_N$ and variances $\sigma_1^2$, $\ldots$, $\sigma_N^2$....
MLS's user avatar
  • 738
4 votes
1 answer

Given two independent normal random variables $X$ and $Y$, what is $P(X\leq x\mid X>Y)$?

As the title says, I'm looking for the distribution of $X$ given that $X>Y$.
Jaho's user avatar
  • 41
1 vote
2 answers

What test to use to find the probability of highest value?

If I have a vector of around 40 values each with a normally distributed error, is there an easy way to figure out the probability of each element being the element with maximal true value? For context,...
Oscar Smith's user avatar
9 votes
2 answers

Rate at which a Gaussian random variable is the maximum in a set of independent Gaussian random variables [duplicate]

Assume a random vector $X = [x_1, x_2, ..., x_n]$ where the random variables are independent and Gaussian distributed. At the same time, they are not identically distributed; they can have arbitrary ...
Chris's user avatar
  • 201
3 votes
1 answer

Tail bounds on a function of normally distributed variables

I am looking for tail bounds (both at $0$ and at $\infty$) for $$ Z:=\exp \left(\frac{\alpha}{4}(X-Y)^2+\frac{\alpha}{2}(X+Y)\right)$$ where $\alpha$ is a positive real and $X,Y$ are i.i.d. normal ...
Sven Stodtmann's user avatar
2 votes
1 answer

Probability of maximum of summed normal random variables

Given four random variables, A,B,C,D, chosen independently from the same normal distribution (with mean $\mu$ and standard deviation $\sigma$), I am trying to solve: $$P[(2+A+B)>(1+B+C) \cap (2+A+B)...
redantu's user avatar
  • 23
1 vote
1 answer

Computing the probability $P(\exists X\in\{X_1,\ldots, X_N\}:X>\text{max}\{Y_1,\ldots, Y_M\})$

I am trying to somewhat generalize a question, which has been asked in one way or another a several times here on StackExchange**. However, I have not managed to find an answer to the below problem. ...
quantB's user avatar
  • 11
1 vote
1 answer

Determining ranking probabilities from overlapping distributions

I'm thinking about coding a ranking engine, and am unclear about how I can combine probability distributions for two (or more) entities. I think this is easier to ask with an example. Say I have two ...
Hobo's user avatar
  • 119
0 votes
0 answers

Probability that a normal RV is greater than multiple other normal RVs

Let $X_1, X_2, ... X_n$ be independently drawn from different normal distributions, such that $ X_i \sim N(\mu_i, \sigma^2_i) $ For any $j$ what is the probability that $X_j$ is the greater than all ...
Andreas's user avatar