# Questions tagged [probability]

For basic questions about probability and the questions associated with the calculation of probability, expected value, variance, standard deviation, or similar statistical quantities. For questions about the theoretical footing of probability (especially using [tag:measure-theory]), ask under [tag:probability-theory] instead. For questions about specific probability distributions, use [tag:probability-distributions] instead.

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11 views

### Number of questions to attend to pass a multiple choice test

There are 100 multiple choice questions in a test, with 4 options each. The probability of choosing a right answer for a question is 0.25 Each right answer gets 4 marks and each wrong answer gets -1 ...
29 views

### What is the probability of finding 2 in set of primes?

Let $$S=\{p :p\in\mathbb{P}\}$$ Be the set of primes. So $2$ is also a member of it right? $$P[\text{ finding 2 in S}]=\frac{1}{\infty}=0 ??$$ Does that mean that probability of finding $2$ from the ...
38 views

### Is there any difference between the two limits in $(1)$ and $(2)$ as above?

I read a a paper about statistics and machine learning ("High-dimensional Asymptotics of Langevin Dynamics in Spiked Matrix Models"). Assume that $\{(Y_0^i, \sqrt{N}U^i)\}_{1\le i\le N}$ are ...
1 vote
26 views

### You and your friend are each dealt two cards: hers face up and yours face down. Which of the following scenarios are you more likely to have a pair?

I am self-teaching probability, could someone please help me determine if I've solved this problem correctly, as I don't have the answers to these exercises. The following question is taken from ...
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### Finding a value to prove a probability mass function.

Ive been given the probability mass function: Pr(X = x) = A(6.75x - x^2) (equation 1) with x ∈ {1,2,3,4,5} and I need to go about finding the value for A so that the probability mass function ...
6 views

### Gibbs sampling from Multinomial distribution

I need to use Gibbs sampling to sample from $(X_1, X_2, \ldots, X_n)$ that is distributed according to Mult $\left( N, 1/n, \ldots, 1/n\right)$. For this I need to compute the conditional pmf ...
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### Why is it impossible to solve the heat diffusion/conduction equation as a function of time in 2D and 3D situations?

The current literature provides solutions for heat diffusion/conduct PDE only for a 1D geometric space plus time dimensions. Why there are no 2D and 3D spatial dimensions plus time. Are mathematical ...
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### CLT and unknown probability of success

Suppose that I distribute flyers on the street and people, when approached, take them with the same probability $p$. On average, I need 5 hours to distribute 2500 flyers and with confidence 0.9 it is ...
21 views

### Why are Some Probability Distributions "Used More Often" for Certain Things?

I have had this question for a long time - Why are Some Probability Distributions "Used More Often" for Certain Things? I understand that for certain problems, the type of probability ...
22 views

### Find $P(W_1 > 1 \cap W_2 < 1)$ where $W_t$ is a standard Brownian motion.

Let $W_t$ be a standard Brownian motion. Find $P(W_1 > 1 \cap W_2 < 1)$. I tried to do something on my own, but because I'm new to Brownian motion, I'm stuck at the beginning of the calculations....
30 views

### Expected number of rounds to reach an intersection size

Consider the set $U=\{1,..,n\}$, and $A=\phi$ and $B=\phi$ are two empty sets to begin. Perform the following step. Choose $m$ elements from $U$ uniformly at random (with replacement) and add to $A$. ...
39 views

### a symmetrical die is thrown, then a coin is thrown as many times as the die indicates .

Exercices : a symmetrical die is thrown, then a coin is thrown as many times as the die indicates points. let $X$ be the number of Tails obtained . Determine $E(X)$ My attempts : First it's clearly ...
29 views

### flip a coin, if head, Z = X, if tail, Z = Y. X, Y if normal distribution (0, 1). what is the probability density function of Z? [closed]

I am trying to solve the following probability problem: Suppose $X\sim N(0, 1)$ and $Y\sim N(0, 4)$. A fair coin is flipped independently from $X$ and $Y$ and define $Z = X$ if if head comes up and ...
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### What is the probability that Camilla and Cameron are paired with each other?

Textbook problem: A teacher with a math class of 20 students randomly pairs the students to take a test. What is the probability that Camilla and Cameron, two students in the class, are paired with ...
1 vote
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### How to proof Lip-constant weakens when size of function class approaches to infinity?

Taken from paper "A Universal Law of Robustness via isoperimetry" by Bubeck and Sellke. Theorem 3. Let $\mathcal{F}$ be a class of functions from $\mathbb{R}^{d} \rightarrow \mathbb{R}$ and ...
23 views

### What is the probability that no one waits for remainder? [closed]

The problem is: There are 20 people in a queue. 10 of them have 10 euro and the others have 20 euro. Everyone wants to buy a ticket that costs 10 euro. What is the probability that no one waits for ...
6 views

### What is the criterium for matrices of real numbers to be a variance-covariance matrix for some random variables

Variance-Covariance matrix of random variables $X_1, X_2, \dots, X_n$ is $\Sigma \in R^{n\times n}$, where $[\Sigma]_{i, j} = Cov(X_i, X_j)$. I'm curious if most of matrices can be the variance-...
24 views

### Proving convergence of $\frac{1}{n}W_n^\top W_n$ where $W_n\sim \mathrm{Mul}(n, \frac{1}{n}1_n)$

I want to prove $$\frac{1}{n}W_n^\top W_n \to2 \qquad \text{in probability.}$$ $W_n$ is a $n\times1$ vector st $W_n\sim \mathrm{Multinomial}(n, \frac{1}{n}1_n)$. I tried to find an upper bound of the ...
1 vote
50 views

### If $X$ and $Y$ are independent, is it true that $\mathbb P (X+Y>x | X+Y>0) \geq \mathbb P (Y>x | Y>0)$ for every $x>0$?

$Y$ is a random variable with symmetric distribution around 0 and both random variables are continuous with existing density It seems true, because the random variable $X$ should just bring further ...
1 vote
27 views

### Markov umbrellas

"I have $4$ umbrellas randomly distributed between my house and my office. Each day I go from my house to the office and back. If it's raining, i will take an umbrella in my way to the other ...
13 views

### How to deal with overflows while using either Welford's or Youngs-Cramper algorithms for variance?

I'm trying to use either of the mentioned algorithms to calculate sample variance. However I ran into this problem -- Welford's algorithm uses for accumulations a sum of differences of elements and ...
20 views

### Bound on entropy of n variables

Let $X_1,X_2,\dots,X_n$ be arbitrary discrete random variables. Prove that $$H(X_1^n)\leq\frac{1}{n-1}\sum_{i=1}^nH(X_1^{i-1},X_{i+1}^n),$$ where for $j\geq i$, $X_i^j$ denotes the block of random ...
41 views

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### Can anyone please assist me with this question using inverse Laplace [closed]

[** Inverse of Laplace**] : https://i.stack.imgur.com/l7c1Z.jpg Inverse Laplace
35 views

### Expected number of self-avoiding walks of a given length in a random graph

Let us consider the following random locally finite (i.e., every vertex has a finite degree) graph: $\mathbb{Z}^d$ ($d\geq2$) is the set of vertices and any two vertices $v$ and $w$ have an edge ...
1 vote
26 views

### Finding stationary distribution of random process

Suppose we are given $x_t, \bar{x_t}, t\in \mathbb{Z_+}$ independent 2-states $\{0, 1\}$ Markov chains with positive transition probabilities. Initial states are $x_0 = 0; \bar{x}_0 = 1$. For which ...
1 vote
Let $B_t$ be Brownian motion for $t\ge0$ so that $B_t-B_s \sim N(0,t-s)$. There are a few formulae out there that show how the $p$-th moment of $E[(B_t-B_s)^p]$ is calculated. My question is: how do ...