This tag is for basic questions about probability and for questions in which one wants to calculate a probability, expected value, variance, standard deviation, or similar quantity. For questions about the theoretical footing of probability (especially using measure theory), please ask under ...

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Find the probability of the following event.

Bayesylvania is awash with citizens not all of whom can be trusted to tell the truth. A traveler finds himself at a T-junction in an area populated by the Asciis and Bisciis in the ratio 11 to 5. A ...
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1answer
7 views

Expected coverage after repeated samples of size $n$

I have a set $S$ of $n$ elements, from which I repeatedly sample $m$ elements. Each of the individual samples are without replacement (so $n$ choose $m$), but they all choose from the full set. Given ...
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0answers
5 views

Unbiased estimator geometric distribution of probability parameter

I am trying to identify an unbiased estimator of the probability parameter $p$ of the geometric distribution, but have only been able to find one - found here as Example 4. Can someone suggest another ...
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1answer
10 views

How much is it worth to participate in a second price auction?

You have a valuation for an object (say $v_a$), which you don't know yet but you know is distributed U[0,1]. You will be competing in a second price auction against a completely identical guy as you, ...
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1answer
16 views

If $X$ has density, when has $X\cdot I_A$ a density?

Let $(\Omega, \mathcal F, P)$ be a probability space, and $X$ be a random variable with some density function $f_X$. If $A \in \mathcal F$, then the indicator function $I_A$ has, as a discrete random ...
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1answer
14 views

Does it hold $\sigma(X_1,\ldots,X_n)=\sigma(X_n-X_1,\ldots,X_n-X_n)$?

Let $(\Omega,\mathcal{A})$ and $(\Omega',\mathcal{A}')$ be measurable spaces $X_1,\ldots,X_n$ be measurable with respect to $\mathcal{A}$-$\mathcal{A}'$ $Y_m:=X_n-X_m$ for $1\le m\le n$ I'm ...
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2answers
9 views

Coupon Collector Problem: probability of an r on the nth roll of k-sided die?

How do I calculate the probability of rolling an r on the nth -- and only the nth -- throw of a k-sided fair die?
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0answers
22 views

$3$-player card game probability question

Three people, (call them $C$, $D$, and $E$), decide to play a card game for fun. They use an ordinary fair deck of $52$ cards, shuffled well immediately before each hand is drawn, and randomly draw ...
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0answers
14 views

Probability problemos

A circuit has three major components, $A, B$ and $C$. A component $A$ operates independently of $B$ and $C$, the components $B$ and $C$ are interdependent. It is known that the component $A$ works ...
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0answers
6 views

Cramér Lundberg Risk Model - exponential distribution of claim sizes

I am studying the classical ruin model, which express the insurance company free surplus at time $t$ as $C_t=u+ct-\sum_{i=1}^{N(t)}Y_i $ where: $ct$ is the premium income up to time t $u$ is the ...
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1answer
19 views

Uncertain about which probability method to use for the problem

Suppose I want to catch a bus (which runs every 10 minutes on average). What is the probability that: 1). You will wait for at least fifteen minutes before the bus arrives, and then, 2). 3 buses ...
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1answer
19 views

Conditional expectation on Bi variate probability distribution

Two balls are drawn simultaneously from an urn containing 2$0$ balls numbered $1,2,3...20$. let $X$ be the number on one of the drawn ball and $Y$ be the number on the other. Find $E(XY)$. I try to ...
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1answer
23 views

A probability problem [on hold]

If it is confirmed that two thirds of the students of C.O.E. Minna are female, calculate the probability that on entering the college, the first two students one meets are: 1. The same gender 2. ...
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2answers
23 views

Find the probability of the following event

You witness a nighttime hit-and-run accident involving a taxi in a city in which 9 out of 10 taxis are green, and all other taxis are blue. Discrimination between the two colours is 80% reliable under ...
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0answers
25 views

Expectation of squared Ito integral

Let $\omega$ be a standard Brownian motion. How do you compute the expectation involving the square of an Ito integral: $ ...
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1answer
41 views

Probability confusing question

I saw this in my probability class past exam papers I saw the answer key but I still can't fully understand. I wish somebody can walk through this with me :) A company takes out an insurance policy ...
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0answers
27 views

Exponent - Solving for an unknown within an expectation

I have reached a stage where I need to solve for an unknown number, $\theta$ . However, I stuck and don't know how to proceed further. The equation to be solved is: $E\left[ \exp(\theta a^i) * ...
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0answers
17 views

The independence of 3 positive events [on hold]

Let $A, B ,C$ be 3 positive events. Suppose $A$ is independent of $B$ and $B$ is independent of $C$. Does $A$ independent of $C$
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0answers
10 views

Calculate the pdf from covariance matrix

I tried to solve the following problem: mu,C are mean vector and covariance matrix of three-dimensional Gaussian random vector X. C(3x3) , mu(3x1). And Y=AX+b where A is 2x3 matrix , b: 2x1 vector ...
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0answers
13 views

Relevant Distribution

I have a 7 year data set with revenue, revenue growth percentage, ebitda liabilities and assets. I have been asked to find the underlying relevant distribution used in the above data set. I'm drawing ...
0
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1answer
11 views

Expected value of characteristic function

I was wondering about the expected value of the characteristic function $\chi_A$ for some set $A \in \mathcal{A}$ in a probability space $(\Omega, \mathcal{A}, \mathbb{P})$. It should be ...
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0answers
65 views

The Lost Boarding Pass Advanced

The Lost Boarding Pass is a famous puzzle as follows: On a sold out flight, $100$ people line up to board the plane. The first passenger in the line has lost his boarding pass, but was allowed in, ...
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1answer
24 views

Calculating the distribution of a compound random variable

Given $X\sim U(1, 0)$ and $Y\sim Exp(1)$, determine the density function of $Z:=\frac{X}{Y}$. Now, without looking up how to do it I tried to figure it out myself. The value of the density function ...
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0answers
12 views

Statistical uncertainty on a percentages inferred from an A/B test

Question: What is the statistical uncertainty on percentages inferred from an A/B test? Example: $N = 100$ people are presented with an A/B choice (e.g., jumping into shark-infested water, choosing ...
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0answers
24 views

Chi-square test of independence: show that sum of squared standard normals has chi-square distribution

I'm studying the chi-square test of independence. According to my understanding, we first hypothesize independence between variables and consider them as being normally distributed. Then we go on to ...
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1answer
27 views

Probability Question Simple Qns

Assume each of the four users is active for 20% of time and data generation rate of the four users are 400kbps, 600kbps, 700kbps and 800kbps, respectively. Calculate the probability that the data ...
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1answer
12 views

Coversion of Probabilities based on time

QUESTION If a shooting star has an 80% chance of appearing in the next hour, what is the chance of it appearing in the next half hour? How does one go about finding probabilities such as this? ...
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2answers
50 views

Probability of a double-headed coin

Here are three related problems from Blitzstein and Hwang's Introduction to Probability. Curious if my approach is sound. I'm reasonably confident in the first result, but not so much in the other ...
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0answers
10 views

“Distance” of iid gaussian variables

Take two i.i.d. Gaussian R.V.s $X$ are $Y$ both of which are $~N(0,a\sigma)$. Define a new R.V. $D = \sqrt{X^2 + Y^2}$. What's the expected value $E(D)$? In researching this I'm seeing references ...
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0answers
11 views

Definition of rough path

There are many books and notes on the rough path theory. A rough path is defined as an ordered pair $(X, \mathbb X)$, where $X$ is a path mapping from $[0, T]$ to some Banach space $V$ and $\mathbb X: ...
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3answers
29 views

Cricket Probability question

My understanding of probability is little weak, and it was since high school I am struggling with it.This question struck me yesterday while watching IPL. ... In a normal game of cricket, there are ...
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0answers
15 views

Bayesian Estimation of the mean of a multi-variate Gaussian

The posterior mean of a multivariate normal distribution is to be estimated with the Bayes rule for densities (http://www.math.uah.edu/stat/dist/Conditional.html), following the approach as described ...
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1answer
15 views

Joint distribution function from marginals

Is it possible to obtain joint distribution function when only the marginal distribution functions of random variables are given and, the random variables are not independent? If possible, it would ...
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0answers
33 views

PROBABILITY PROBLEM PLEASE HELP ASAP [on hold]

if you selected the numbers 1,2 ,3 and 4 at random. That is you selected then in some way so that each number was equally likely to be chosen- what is the probability of getting a fraction sum that ...
2
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2answers
22 views

Probability of sorting at least one correctly

If I have 5 balls label 1 through 5, to put one in each of 5 boxes also labeled 1 through 5. What is the probability of putting at least one ball in it's matching box? My first approach was to ...
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0answers
14 views

Conditional expectations with identical marginals and positively dependent but unknown joint distribution

Let $A$ and $B$ be random variables, each with marginal distribution $% U\left( 0,1\right) $, but unknown joint distribution $H\left( a,b\right) $. Suppose $A$ and $B$ are each stochastically (weakly) ...
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2answers
18 views

Joint Probability density function

Two components in rocket operate independently and the probability that each component fail is p. Let X denote the number of launches require to have a failure of component 1 and Y denote the number ...
2
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2answers
28 views

Can there exist $3$, $4$ and $5$-faceted shapes with congruent flat sides in $\mathbb{R}^3$?

I rose this question in my discrete math class (the unit on probability) not too long ago. For instance, a two-sided shape (like a coin) can be one with any geometrical shape as its "side," such as a ...
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1answer
20 views

Conditional probability distribution notation versus conditional probabilities of a single sample space?

When writing conditional marginal probabilities, the following seems to be the notation: $$p_{i|Y=y_{j}} = P(X=x_{i}|Y=y_{j}) = \frac{P(X=x_{i},Y=y_{j})}{P(Y=y_{j})}=\frac{p_{ij}}{p_{+j}}$$ This is ...
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0answers
36 views

Expected costs, benefits of a test [on hold]

The president of a firm in a highly competitive industry believes that an employee of the company is providing confidential information to the competition. She is 90% certain that this informer is the ...
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0answers
14 views

Unbiased estimator for geometric distribution parameter p

I believe that the MLE of parameter $p$ in the geometric distribution, $\hat p = 1/(\bar x +1)$, is an unbiased estimator for $p$ and would like to prove it. So far, I have: $E[\bar x + 1] = E[\bar ...
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1answer
23 views

which choice is better?

Lets say you were writing a program to play checkers. Im simplifying the numbers, but the gist should be obvious. Your program calculates the odds of Move A to have a 100 chances to win the game and ...
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2answers
49 views

Probability of segment lying in circle

Given a circle of radius R: $x^2+y^2\le R$, find probability of horizontal segment with length $\frac{R}{2}$ lie whole inside this circle. Position of segment's center has uniform distribution in ...
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0answers
27 views

Markov Chain problem application

Let $P$ be the transition matrix for a regular Markov chain and $v$ be its equilibruim vector. Show that $v$ has zero entries. How would you prove this? I am struggling in this class. Any help is ...
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0answers
75 views

Random walk, expectation & variance, joint probability, approximation question [on hold]

Consider the following random walk on a plane: The walk commences at the origin and at each timestep, a step of unit length is taken in a random direction $\theta$ (measured relative to the positive x ...
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0answers
9 views

(Empirical likelihood method) Find the order of a parameter given a set of constraints

Firstly we assume that $X_1,...X_n$ are order statistics($X_i\leq X_{i+1}$) from an i.i.d sample of random variables and let $r$ be integer and $r\geq1$. Start with the equation (1) \begin{equation} ...
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0answers
20 views

Almost sure closeness of random elements in a Hilbert space

Suppose I have a probability space $(\Omega,\mathscr{F},\mathbb{P})$ and a probability measure $\eta$ on a separable Hilbert space $H$ endowed with the Borel $\sigma$-algebra $\mathscr{B}$ arising ...
2
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2answers
34 views

Expected value with negative exponent

I am trying to solve identify the expected value of a statistic that involves a fraction. I have simplified the expression to: $E[\frac{1}{1+ \sum_i x_i}] = E[\frac{1}{1+ T}]$ However, I am not sure ...
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1answer
19 views

Doubtful answer for conditional probability question

There's a traffic light in a city which works properly, but sometimes it is faulty. If it functions properly today, there is a 95% chance that it will not malfunction tomorrow. However, if it is ...
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0answers
38 views

Expected number of rolls on a 200 sided die to roll a 1? [duplicate]

We have a 200 sided fair die with faces numbered 1 through 200 and want to know how many rolls are expected to roll a 1. How would I go about calculating this?