Tagged Questions

0
votes
0answers
16 views

Random variables resulting due to single or multiple experiments

Assume there are ‘n’ entities that collect some data after each ‘t’ time instances. Generally their collected data is within an “expected” range. However, occasionally the data exceeds the “expected” ...
0
votes
0answers
25 views

Probability that a given Normal Distribution is Maximum among others [duplicate]

You are given the mean and standard deviations of N normal distributions x1,x2...xn What is the probability that x1 is maximum? ie. Find P(x1>x2,x3..xn) How do I go about solving this? x1,x2,x3 etc ...
1
vote
1answer
74 views

How to calculate minimum of multiple exponential distributions?

$X_1$, $X_2$, $X_3$ are independent random variables, each with an exponential distribution, but with means of $2.0, 5.0, 10.0$ respectively. Let $Y$= the smallest or minimum value of these three ...
2
votes
0answers
25 views

Estimating the likelihood of independence of two discrete variables using the co-occurrence count matrix

I have some data about users from different regions visiting different directories of some website. Aggregating that data I get the co-occurrence frequency matrix (for regions and directories). Now I ...
0
votes
2answers
130 views

How to compute the PDF of a sum of a discrete and a continuous random variable? [closed]

I have a problem with this exercise in probability and statistics: Calculate the probability density function (PDF) of $$Z=X+Y$$ where $Y$ is discrete random variable which is equal to $-1$ and $1$ ...
1
vote
1answer
48 views

Does this break down adding independent probabilities?

I was thinking about this today so I decided to ask it here. I know the rule of adding probabilities. As I was taught in grade school "OR" typically means add and "AND" typically means multiply. ...
2
votes
1answer
247 views

Expected value of modified geometric distribution

I am trying to find the expected value of $X$, where $X$ is the number of orders a customer will make in a lifetime. Assuming that there is a $p=.1$ chance of the customer placing an initial order, ...
3
votes
2answers
178 views

What is $P(X_1>X_2 , X_1>X_3,… , X_1>X_n)$?

All $X$ are mutually independent and from normal distributions, each with its own mean and variance. If it's easier, $P(X_1 \geq X_i \forall i \in \{1, ..., n\})$ is fine although I suspect it's the ...
2
votes
1answer
122 views

Product of Independent Gaussian Variables

Let $X$ and $Y$ be two independent normal distributions according to $X\sim\mathcal{N}(0,P)$ and $Y\sim\mathcal{N}(0,Q)$. Is it true to say the following ? ...
2
votes
1answer
104 views

“Running it” multiple times in No-Limit Hold'em poker

Suppose on the flop in no limit hold'em two players go all-in. They both have 2 hole cards and there's 3 community cards on the board at present. There will be 2 more cards drawn and each player will ...
0
votes
1answer
144 views

CDF in Discrete Simulation (Jerry banks book)

Consider the experiment of tossing a single die. Let X be number of spots on up face of die after toss. Then range space of X is Rx = { 1,2,3,4,5,6}. The discrete probability distribution for this ...
1
vote
1answer
301 views

Composition of probability density

I know probability distribution for parameter $\phi$. I have the empirical distribution/statistical distribution of $X$ that is dependent on parameter $\phi$ for $\phi \in [0,1]$. I assimilate this ...
3
votes
0answers
147 views

Probability distribution for transformation of a random variable

Let $g(x)=1$ if $x \leq c$ and $g(x)=(1-x)/(1-c)$, where $0 \leq x \leq 1$ and $0 <c <1$. So $g$ is an non-increasing function. Define $g^{-1}(y)=\inf\{0 \leq x \leq 1 \mid g(x) \leq y\}$. ...
1
vote
1answer
98 views

Are the products of different independent random variables independent?

I'm confused about the independence of the product of independent random variables. Let A and B be independent of each other ...
5
votes
1answer
551 views

How to show that polar coordinates in a uniform distribution on a disk are independent?

Let the random point $(X,Y)$ be uniformly distributed on the unit disc $D=\{(x,y):x^{2}+y^{2}<1\}$. Show that the polar coordinates $R\in [0,1)$ and $\theta \in [0,2\pi)$ of the point are ...
-3
votes
1answer
166 views

Pairwise vs. total independence of discrete uniform random deviates

Let $X$ be a discrete uniform random variable on the set $\{000, 011, 101, 110\}$ of four binary integers, and let $X_{i}$ denote the ith digit of $X$, for $i = 1, 2, 3$. Show that $X_{1}, X_{2}, ...
0
votes
0answers
55 views

Random Variable as a function of mean probability

Suppose that in a real communication system we make a scheduling decision $\omega$ at any time slot $t$ that affects the probability of loss of a packet (i.e. the probability of loss depends on our ...
-1
votes
1answer
101 views

A function of Bernoulli variables?

Let $X_1,X_2,...,X_n$ be a fixed number of Bernoulli random variables. My problem is to find a distribution for $Y$ such that for some function $f$, we have $Y=f(X_1,X_2,...,X_n)$. There are two ...
2
votes
2answers
168 views

$E(\min_{1 \leq i \leq m} |x - y_i|)$

I have faced a statistical problem in a computational biology question. I will explain it in statistical language. Let's say we have the results of rolling one red die, $x$, and $m$ black dice ...
0
votes
1answer
80 views

What is the probability of observing not more than N positive outcomes

I have the population which is split into three classes; A, B and C. We know that the number of observations in each class is Na, Nb and Nc respectively. Assuming that my observations are binary ...
6
votes
1answer
481 views

Notation conventions for random variables and their distributions

I get confused on the proper notations of meanings, as well as the meanings of some notations relating to random variables and their distributions. Below, I will list things that I think are true, as ...
8
votes
2answers
494 views

Are the random variables $X$ and $f(X)$ dependent?

Can we say anything about the dependence of a random variable and a function of a random variable? For example is $X^2$ dependent on $X$?
5
votes
1answer
494 views

How to define a distribution such that draws from it correlate with a draw from another pre-specified distribution?

How do I define the distribution of a random variable $Y$ such that a draw from $Y$ has correlation $\rho$ with $x_1$, where $x_1$ is a single draw from a distribution with cumulative distribution ...
7
votes
1answer
441 views

In convergence in probability or a.s. convergence w.r.t which measure is the probability?

I was presenting proofs of WLLN and a version of SLLN (assuming bounded 4th central moment) when somebody asked which measure is the probability with respect too and I realised that, on reflection, I ...
2
votes
1answer
110 views

Few random variables cannot influence $n$ independent others too much?

I have $n$ standard normal and independent random variables $X_i$ (In reality I have a large known number of them, but let's just say I have $n$). In my experiment I want to on average get exactly 3 ...
4
votes
2answers
478 views

Is there a relationship between the median of a function of random variables and the function of the median of random variables?

Background notation: RV= random variable, $\mu=$ mean $m=$ median Jensen's Inequality considers the relationship between the mean of a function of an RV and the function of the mean of an RV. If ...
17
votes
5answers
3k views

Convergence in probability vs. almost sure convergence

I've never really grokked the difference between these two measures of convergence. (Or, in fact, any of the different types of convergence, but I mention these two in particular because of the Weak ...