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.
87,005
questions
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1answer
387 views
Normal distribution probability
just a quick question dealing with probability. The annual returns on stocks and treasury bonds over the next 12 months are uncertain. Suppose that these returns can be described by normal ...
1
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1answer
19k views
Probability increases as sample size increases?
I was talking with a friend and we were discussing a math problem disguised as a social situation:
If the chance that someone to accept your request to go out with them was 1% and you asked 1 person ...
5
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3answers
5k views
How many right angled triangles can a circle have?
Here's what I recall of the question from CNML Grade 11, 2010/2011 Contest #3, Question 7:
There are 2010 points on a circle,
evenly spaced. Ford Prefect will*
randomly choose three points on ...
8
votes
3answers
208 views
Asymptotic behavior of the first step in a best strategy
Consider the game described here, but for a sequence $X_1,\ldots,X_n$ of i.i.d. uniform rv's on $\lbrace 1,\ldots,n \rbrace$ (in the original game $n=6$). Using the original notation, let $a_n$ denote ...
13
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3answers
2k views
Best Strategy for a die game
You are allowed to roll a die up to six times. Anytime you stop, you get the dollar amount of the face value of your last roll.
Question: What is the best strategy?
According to my calculation, for ...
1
vote
2answers
177 views
How to select the optimum combination of numbers from a random list that add to up to a certain total (or as close to)
I'm developing a computer program, and need an algorithm to solve the following problem:
How to select the optimum combination of numbers from a random list that add to up to a certain total (or as ...
2
votes
1answer
2k views
Uniform White Noise
I found a contradiction I couldn't resolve by my self.
It's about a "Uniform White Noise".
Let ${x}_{t}$ be a "White Noise" i.i.d. Random Process:
$ \forall t \in \mathbb{R}, \ {x}_{t} \sim U[-1, ...
23
votes
6answers
31k views
Average length of the longest segment
This post is related to a previous SE post If a 1 meter rope ā¦. concerning average length of a smallest segment.
A rope of 1m is divided into three pieces by two random points. Find the average ...
2
votes
1answer
167 views
Probability of the sum of n numbers giving the same last d digits
Can anybody give me a hint how to approach the following problem, please?
I actually am having a hard time stating the problem. I think an example would help you understand what the problem is.
...
14
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6answers
14k views
Probability of picking a random natural number
I randomly pick a natural number n. Assuming that I would have picked each number with the same probability, what was the probability for me to pick n before I did it?
0
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4answers
284 views
What probability distribution is this?
This image show a histogram (200 bins) of accumulated distances from a radar distance meter (very noisy).
The peak around 7 meters is an object. At thought this looked kind of like a normal ...
2
votes
1answer
239 views
How to calculate likelihood to succeed knowing attempts and successful attempts amounts?
Say I have two algorithms that I don't know how they work but I know what they are meant to achieve. I tried algorithm A once and it succeeded. And tried algorithm B 100 times and succeeded 99 times. ...
0
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2answers
250 views
Doubt in a probability problem
Problem:
Alex flip a fair coin three times. what is the probability that she gets two heads given that the first is a head?
My solution is based on the argument that from the given information the ...
46
votes
10answers
32k views
If a 1 meter rope is cut at two uniformly randomly chosen points, what is the average length of the smallest piece?
If a $1$ meter rope is cut at two uniformly randomly chosen points (to give three pieces), what is the average length of the smallest piece?
I got this question as a mathematical puzzle from a friend....
2
votes
2answers
2k views
Are these transformations of the $\beta^\prime$ distribution from $\beta$ and to $F$ correct?
Motivation
I have a prior on a random variable $X\sim \beta(\alpha,\beta)$ but I need to transform the variable to $Y=\frac{X}{1-X}$, for use in an analysis and I would like to know the distribution ...
2
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1answer
378 views
Reducing quantification to probability
I was thinking about some problem involving quantifiers (the existencial and universal quantifiers) and I noticed how it might resemble probability in a sense. They both assume a variable and its ...
0
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1answer
2k views
density function by the method of transformations
We have a random variable $Y$ that has a uniform distribution on the interval $[1,5]$. The cost of delay is given by $U = 2Y^2 + 3$. Use the method of transformations to derive the density function of ...
1
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4answers
869 views
Probability Problems
Problem:
The probability that a man who is 85 years. old will die before attaining the age of 90 is $\frac13$. A,B,C,D are four person who are 85 years old. what is the probability that A will die ...
2
votes
2answers
137 views
Doubts on a probability problem
Problem:
From the deck of the 52 cards,cards are drawn randomly without replacement.What is the probability of drawing a king of hearts at the third attempt? If it was drawn at the 15th attempt, what ...
9
votes
1answer
10k views
martingale and filtration
As I understand, martingale is a stochastic process (i.e., a sequence of random variables) such that the conditional expected value of an observation at some time $t$, given all the observations up to ...
2
votes
3answers
3k views
binomial random variable
Let $Y$ be a binomial random variable with $n$ trials and probability of success given by $p$. Show that $n-Y$ is a binomial random variable with $n$ trials and probability of success given by $1-p$.
...
2
votes
1answer
3k views
statistics - moment-generating function
Let $Y_1,\dots,Y_n$ be independent and identically distributed random variables such that for $0 < p < 1$, $P(Y_i = 1) = p$ and $P(Y_i = 0) = q = 1-p$.
A. Find the moment-generating functions ...
6
votes
0answers
440 views
An application of the Optional Sampling Theorem
let $S(k), k\geq 0$ a discrete random process. Suppose $S(N)$ is with probability one either 100 or 0 and that $S(0)=50$. Suppose further there is at least a sixty percent probability that the price ...
6
votes
1answer
357 views
Negativity in a CIR model discretized by Ito-Taylor expansion
Let $X = (X_t: t \in [0,T])$ be a stochastic process satisfying a CIR model
$$
dX_t = \beta (X_t - \gamma) dt + \sigma\sqrt{X_t} dB_t,
$$
where $B_t$ is a standard Brownian motion, $\beta$ is a ...
2
votes
1answer
529 views
distribution of iid sequence of integrable random variables
I came across an interesting problem in Jacod's probability book. But have no idea how to approach it. Should I approach it using induction? Any ideas?
Let $X_1, X_2, \cdots$ be an infinite sequence ...
3
votes
1answer
12k views
Find an unbiased estimate for Ī»s (Poisson distribution)
So I have this problem to solve...
Let X denote the number of paint defects found in a square yard section of a car body painted by a robot.
These data are obtained:
8, 5, 0, 10, 0, 3, 1, 12, 2, 7, ...
6
votes
1answer
5k views
Doubts on Mutually exclusive and Independent events
Problem:
In a school competition,the probability of hitting the target bu Dick is $\frac{1}{2}$,by Betty is $\frac{1}{3}$ and by Joe is $\frac{3}{5}$.If all of them fire independently,calculate the ...
3
votes
3answers
1k views
Density of a function of random variables
I recently learned about finding density functions of functions of random variables using the cumulative distribution function. For example, computing the density function for the difference of two ...
4
votes
1answer
3k views
Statistical Inference Question
From Statistical Inference Second Edition (George Casella, Roger L. Berger)
"My telephone rings 12 times each week, the calls being randomly distributed among the 7 days. What is the probability that ...
4
votes
2answers
3k views
A continuous analogue of the binomial distribution
For any positive integer $N$, the binomial$(N!,p)$ distribution has the following property: for any $1 \leq n \leq N$,
there exist i.i.d. random variables $X_1,\ldots,X_n$ such that $X_1 + \cdots + ...
1
vote
1answer
209 views
Understanding birthday attack probabilities
I have two sets $M$ and $H$. $M$ is an arbitrary string of length $k$ and $H$ is an string of length $p$. Both are constructed from a charset of length $r$. And $p<k$.
Hash function $f(m)=h$.
I ...
3
votes
1answer
647 views
binomial-Poisson/beta hierarchy
X|N,P ~ Binomial(N, P)
N ~ Poisson(11)
P ~ Beta(2,3)
What is the moment generating function for X?
8
votes
1answer
512 views
Question about Brownian motion
Let $\{B(t), t \in \mathbb{R} \}$ be a two sided brownian motion defined as
$$
B(t) = \begin{cases} B_1(t),\quad t >0 \\
0, \quad t = 0 \\
B_2(-t), \quad t < 0 \end{cases}
$$
where $B_1$ ...
1
vote
1answer
163 views
Risk process in Insurance
Let
$R(t) = u + ct - \sum_{k=1}^{X(t)}Z_{k}, t\geq 0 $,
be a risk process, where $u> 0$ is the initial capital of the insurance company and $c> 0$ is a premium rate. We know that the number of ...
2
votes
3answers
178 views
a simple argument?
This argument appeared in a proof in a paper (I am paraphrasing), and I am not sure why it is true. It should be rather simple.
Let $(\Omega,P)$ be some sample space. Let $X$ be a random variable ...
2
votes
2answers
113 views
probability of heads
What is the probability of getting $3$ heads in a row? Would it be $\frac 18$?
assuming the coin is a fair one.
0
votes
1answer
2k views
density function of U when Y has a beta distribution
Assume that Y has a beta distribution with parameters a and b. Find the density function of U = 1 - Y.
I know how to do then when they give the density function of Y, but i'm confused here.
Thanks!
7
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1answer
3k views
Probability on spreading of rumors
A little help here. Exercise 21, Ch. 2 from Feller's book reads
In a town a $n+1$ inhabitants, a person tells a rumor to a second person, who in turn repeats it to a third person, etc. At each ...
3
votes
3answers
363 views
Gaussian Distribution + Hash Tables
The original question I posted on StackOverflow. I think it's more mathematically inclined so I posted it here again. In terms of math.
There's a class of students. Each students has a score between ...
12
votes
3answers
5k views
How do I Generate Doubly-Stochastic Matrices Uniform Randomly?
A doubly-stochastic matrix is an $n\times n$ matrix $P$ such that
$\displaystyle\sum_{i=1}^n{p_{ij}}=1$
and
$\displaystyle\sum_{j=1}^n{p_{ij}}=1$
where $p_{ij}\ge 0$.
Can someone suggest an ...
0
votes
1answer
93 views
What probability methodology is electronic payment using?
Just curious. You pay electronically, and you get a string of numbers. My question, what is the likelihood for a person to type in the same serial number to say, top up their mobile credit? What is ...
2
votes
1answer
94 views
Continuity of $E[\max(x+Z,0)]$ as a function of $x$
Let $Z$ be a random variable with finite mean and consider the function $F: R \rightarrow R$ defined by $$ F(x) = E[\max(x+Z,0)]$$ How to prove that $F(x)$ is a continuous function of $x$?
This is ...
17
votes
6answers
4k views
Probability of dice sum just greater than 100
Can someone please guide me to a way by which I can solve the following problem.
There is a die and 2 players. Rolling stops as soon as some exceeds 100(not including 100 itself). Hence you have the ...
5
votes
2answers
238 views
Particle moving at constant speed with Poisson setbacks
Consider a particle starting at the the origin and moving along the positive real line at a constant speed of 1. Suppose there is a counter which clicks at random time intervals following the ...
4
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3answers
19k views
probability of getting 50 heads from tossing a coin 100 times
folks,
i am new to this forum and not a math expert. so please bear with me if am asking silly questions.
The question is "probability of getting 50 heads from tossing a coin 100 times".
So the ...
8
votes
4answers
998 views
Probability of the maximum (Levy Stable) random variable in a list being greater than the sum of the rest?
Original post on Mathoverflow here.
Given a list of identical and independently distributed Levy Stable random variables, $(X_0, X_1, \dots, X_{n-1})$, what is the is the probability that the maximum ...
2
votes
2answers
1k views
Given a function $f(x)$ where $x$ is uniformly distributed between $a$ and $b$, how do I find the probability density function of $f$?
For example, if $f(x) = \sin x$ and $x$ is uniformly distributed on $[0, \pi]$, how is the equation found that satisfies the probability distribution function of $f(x)$? I imagine the distribution ...
6
votes
2answers
466 views
expectation of $ \left(\sum_{i=1}^n {x_i} \right)^2 $
If $x_i$ is exponentially distributed $(i=1,...,n)$ with parameter $\lambda$ and $x_i$'s are mutually independent, what is the expectation of
$\left(\sum_{i=1}^n {x_i} \right)^2$
in terms of $n$ and ...
5
votes
2answers
2k views
Does equality in distribution imply equality of expected value?
In other words, if X = Y in distribution, is it true that EX = EY?
I think this must be true, but I've tried to prove it a few times and I always get stuck.
Thanks in advance for any hints or ...
2
votes
1answer
271 views
Maximum value of probability
This is my first post here. Apologies if there are any misformats or mis-tagging.
Also if the post doesn't belong here, sorry, and I will delete it.
I derived this formula from a probability ...
