# Tagged Questions

Questions on using, finding, or otherwise relating to probability distributions, pdfs, cdfs, or the like.

15 views

### Why does the following equality hold in proving Meyer's inequality?

I have a question in proving Meyer's inequality. The proof I read is taken from the book "Malliavin Calculus and related topics" by Nualart. I just have one equality which I am not sure, I will ...
24 views

### Limit theorem for changed time

This post seems long, but its almost everything proofed except the last step. The unknown part is marked especially. Given a Levy-Process $U_{t}$ with with $E(U_t)=0$ (then $U_t$ is a martingale). ...
26 views

23 views

23 views

### Joint probability distribution.

I am trying to calculate P(Y|Z) given the following distribution $\ P(X,Y,Z) = P(X)P(Z)P(Y|X,Z)$ Now, initially I did the following calculation. ...
14 views

### bloom filter: how to estimate probability and tune the filter

My goal is to tune bloom filter in such a way so that I'd get best possible results. I have a dictionary of N=100000 strings, and I have distinct sets of strings S0, S1, S2. For each string from ...
23 views

16 views

### Using the Central Limit Theorem to calculate a mean from Poisson distributed random variables

Firstly, I am studying the basic concepts of statistics and so any explanations, advice and suggestions are more than appreciated. Onto the problem- I am given the central limit theorem and understand ...
34 views

### Birthday line to get ticket in a unique setup

At a movie theater, the whimsical manager announces that a free ticket will be given to the first person in line whose birthday is the same as someone in line who has already bought a ticket. You ...
40 views

### Probability density function for product and minimum of i.i.d. $U(0,1)$ random variables

If $U$ and $Y$ and $Z$ are i.i.d. $U(0,1)$ random variables, find the pdf for $A= U \times Y$ and $B = \min \{ U,Y,Z\}$.
11 views

### What are the differences between stochastic v.s. fixed regressors in linear regression model?

If we have stochastic regressors, we are drawing random pairs $(y_i,\vec{x}_i)$ for a bunch of $i$, the so-called random sample, from a fixed but unknown probabilistic distribution $(y,\vec{x})$. ...
54 views

### Let $X$ be a random variable with mean $0$ and finite variance $\sigma^2$. By applying Markov’s inequality show that

I am looking for confirmation that I am working in the correct direction as well as pointers for points where I have gone astray. Here is the problem. (a) Let $X$ be a random variable with mean $0$ ...
6 views

210 views

### Why was I wrong about the monster-gem riddler

Every week I like to do the fivethirtyeight.com Riddler, an interesting and pleasantly challenging (at least for me) weekly math puzzle which comes out Fridays, with the answer and explanation to the ...
45 views

### Probability Mass Function of infinitely re-rolled dice

I play a game called Shadowrun. It is a role-playing game that uses a dice pool mechanic. A player has a dice pool of $x$ six-sided, unbiased dice. Every 5 or 6 counts as a success. The more ...
260 views

### Condition probability distributions: Two people flipping fair coins

Suppose that two people are playing a game where they each flip a fair coin 100 times. The winner of this game is the person who has flipped the most heads. What is the expected number of heads ...
29 views

### Computing the distribution of a uniform r.v. with parameter being another uniform r.v.

I have this: Let $X\sim U(0,1)$, $Y\sim U(X,1)$. What is the distribution of variable $Y$? My answer: I use a geometric approach since everything happens in the square $(0,1)\times (0,1)$, see ...
12 views

### Relation between Poisson representation of extremes and GPD representation of extremes

I want to derive the theoretical relation between the parameters in a point process model for extremes and the parameters in the GPD model for extremes. I'm following Coles - An introduction to ...
34 views

### On the proof that every positive continuous random variable with the memoryless property is exponentially distributed

The theorem to prove is: $X$ is a positive continuous random variable with the memoryless property, then $X \sim Expo(\lambda)$ for some $\lambda$. The proof is explained in this video, but I will ...
43 views

### How to generate correlated random numbers with specific distributions?

After read the answers of some similar questions on this site, e.g., Generate Correlated Normal Random Variables Generate correlated random numbers precisely I wonder whether such approaches can ...
I am trying to solve the following problem: A box contains N balls: $N_1\ white, N_2\ black,\ and\ N_3\ red\ (N = N_1 + N_2 + N_3).$ A random sample of n balls is selected from the box (without ...