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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7 views

Continuous mapping theorem with density convergence

Let us consider a bivariate random variable $X\in \mathbb{R}^2$ with $pdf$ $f$. Also let, based on a sample of size $n$, let the the estimator of the density be $f_n(x)$ at $x\in \mathbb{R^2}$ and we ...
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1answer
10 views

Let X and Z form a random sample from a poisson dist.If Y=min( X,Z), what is P(Y=1)??

Let X and Z form a random sample of poisson distribution and define Y=min( X and Z) What is P(Y=1)?? I think Y is minimum of two. If X=1, then Z can be any number except 0 If Z=1, then X can be ...
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0answers
15 views

Calculate the probability in order to $f(y)=1$ provided $y\in \mathbb{R}^N$.

Given $x_1,x_2,...,x_n$ be $n$ points in $\mathbb{R}^N$.Let $f:\mathbb{R}^N\rightarrow \left\{ 0,1\right\} $. Suppose that $f(x_1)=f(x_2)=...=f(x_n)=1$. Calculate the probability in order to $f(y)=1$ ...
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1answer
13 views

Comparing Percentiles of 2 Samples Drawn from the Same Distribution

Suppose I have two sets of numbers: $A=\{a_1,a_2,...a_{N_1}\}$ and $B=\{b_1,b_2,...b_{N_2}\}$ with $N_1<N_2$. WLOG assume that $a_i<a_j$ for all $i<j$ and similarly for $b_i$ and $b_j$. ...
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2answers
34 views

Dice Probability (increasing numbers)

If I have 6 regular dice, (each numbered 1-6): What is the probability that when rolled that each will be a different number.(each individual di is a different number from 1-6, but a random order) ...
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1answer
30 views

The probability of a number appearing in an approximation of an irrational number?

I was wondering if for the number Pi some numbers are more likely to appear than others, for example 3.141594 ... The number 1 appears twice does that mean that the probability for the number 1 ...
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1answer
13 views

How to calculate covariance of X and Y given joint probability

$X$ and $Y$ are dependent variables both normally distributed as $N(\mu-const, \sigma^2)$. I don't know what the joint distribution is. I know that when $const = 0$, then the joint probability ...
4
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2answers
27 views

Determining probability generating function for waiting time to see first $SS$

Given a sequence of Bernouilli trials, we have $P(S) = \frac{2}{3}$ with $0<p<1$. The event "SS" occurs on the $i$-th trial if we observe an $S$ on the $i$-th trial following a $S$ on the ...
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0answers
21 views

Combining Markov chains

If the following Markov chain relations hold: $$X \rightarrow Y \rightarrow Z,$$ $$Y \rightarrow W \rightarrow Z,$$ can we combine them to have $$X \rightarrow Y \rightarrow Z \rightarrow W ...
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1answer
22 views

Given probability of two elements being same in a list, find total number of unique elements

I have a list L, of numbers ordered randomly. Every number in the list is from a domain of $1$ to $100$ with the possibility of duplicates. If I point to(without removing) two numbers from the list ...
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3answers
35 views

Normal distribution exercise!

If a technician does not encounters any hardware problems, the time he requires to assemble a computer follows a normal distribution with a mean of $30$ minutes and a standard deviation of $3$ ...
1
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1answer
17 views

Given Nd6, what is the probability that the two highest are minimum 4?

So, my statistics knowledge is rather poor, so I would welcome a formula explanation to the question: given Nd6 (6-sided dice) what is the probability that the two highest numbers are at least a 4? ...
6
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1answer
39 views

Show rigorously that Pólya urn describes a martingale

We work with the famous Pólya urn problem. At the beginning one has $r$ red balls and $b$ blue ball in the urn. After each draw we add $t$ balls of the same color in the urn. $(X_n)_{n \in \mathbb ...
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0answers
50 views

How many from 0 to 99999 [on hold]

How many times does the number 92789 appear in any sequence from 0 - 99999. If you know can you please include the formula.
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1answer
40 views

Probability of a rolling a dice $n$ times with $k$ faces

I need help calculating the probability of rolling $n$ dice with $k$ faces. So you have multiple dice, all with $k$ faces (number of sides on a dice) and you want to calculate the probability of a ...
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3answers
33 views

About discrete probabilities (Expected values)

Is my solution correct? Suppose two player (A and B) each one with 200,00 dollars toss a coin not balanced in a such way that the probability of head is $p$. Suppose yet that if the result obtained ...
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0answers
17 views

Find the constants for the independence of a random variable

The following is my question: Let $W(t)$ be a standard Brownian motion, $\xi\sim N(\mu,\sigma^2)$, and $\xi$ is independent of $W(t)$ for all $t\geq0$. Define $X(t)=t\xi+\lambda W(t)$, for some ...
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1answer
23 views

Markov Chains, reccurent and transient

Let the Markov Chain consisting of the states $0,1,2,3$ have the transition probability matrix ...
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4answers
45 views

Probability question involving infinite number of vertical chords in a 1 inch circle.

Infinite number of vertical chords drawn on a circle with a 1 inch radius. What is the probability that a randomly picked chord is shorter than the radius? The answer should be $1 - .5√ 3$ or ...
2
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0answers
6 views

Likelihood that two markov chains are derived from the same transition matrix

Forgive me for my weak statistic background, hopefully what I'm asking makes sense. So some quick background, I have one markov chain from a data set and many additional chains that I'm producing from ...
2
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1answer
30 views

Does the distribution of a process on $\mathbb{R}^{[0,\infty)}$ uniquely define it?

Question: Can I have two different stochastic processes $(A_t)_{t \in [0, \infty)}$, $(B_t)_{t \in [0, \infty)}$ having the same distribution on $\mathbb{R}^{[0, \infty)}$ differ in some ways? ...
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1answer
42 views

An isosceles right triangle has legs of length 10. A pin is dropped into it and lands somewhere in the triangle where all places are equally likely.

What is the probability that it does not land within 2 units of any of the sides? From my calculations, I get that the smaller triangle has side lengths of 4,4, 4 root 2 (-2 at the right angle and ...
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3answers
144 views

Stumped - How would I solve this probability question?

This question was merely a fun online math problem to see how many people could solve it, but I haven't been able to since last week and it's begiing to drive me nuts. The question: A man has 7 math ...
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0answers
18 views

Distribution of the maximum of correlated Gaussian variables

I try to unterstand how the distribution of the maximum of a iid Gaussian sample changes when we introduce correlation. For this, I simulated iid random samples and correlated samples with $\sigma =1$ ...
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2answers
16 views

Probability of X given the sum

I am given that $X \sim P(\lambda)$, $Y \sim P(\gamma)$, and told to calculate the distribution of $P(X | X+Y = n)$ I proceed as follows $$ \begin{equation} \begin{split} P(X=i|X+Y=n) &= ...
1
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2answers
36 views

How to calculate $V(X+Y)$ with $X$,$Y$ dependent?

I want to calculate the covariance of two dependent variables $X$ and $Y$ and I don't know the value of $V(X+Y)$, that is, the variance of $X+Y$. I know how the quantities relate to each other: ...
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0answers
17 views

nearest point in Poisson point process

Consider a homogeneous Poisson point process in 2D space with density $\lambda$. Consider a sector with an arbitrary origin $o$, angle $0<\theta<2\pi$. What is the PDF of distance from the ...
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0answers
13 views

Question concerning a proof on Stroock and Varadhan 1971

In the proof of theorem 2.3 of the article diffusion processes with boundary conditions (1971) one reads: where $Q_{s,x}$ is the unique solution to the martingale problem for $a,b$ starting from $x$ ...
-3
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1answer
19 views

prior probablity is lower than conditional probabilty [on hold]

Is there any reason behind the fact that prior probability is always lower than the conditional probability? I'm wondering why this happens..Can you please provide any reason for it?
0
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1answer
14 views

Expectation of size of bootstrapped sample

Lets say we have a sample $\mathbf{X} = \{x_1, x_2, \dots, x_N\}$. We draw $N$ points from $\mathbf{X}$ with replacement (do a $\textit{bootstrap})$. What is the expectation of size of bootstrapped ...
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3answers
50 views

Probability Of People Visiting Pubs

5 people went out to pubs. everyone individually choose a pub randomly from 10 pubs available. What is the probability that at "Pub1" "Pub2" came at least one person? $|\Omega|=10^5$ How can ...
3
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2answers
33 views

A grasshopper starts at the origin and is equally likely to hop north,s,e,w. What is the probability that it's coordinates will be 0,0 after 4 hops?

The grasshopper must hop in all $4$ directions (North, South, East, and West) to get back to the origin after $4$ hops. Therefore, I did: $\frac{(4 \cdot 3 \cdot 2 \cdot1)}{4^4} = .09375$. However, ...
0
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0answers
12 views

Finding the factorial moment generating function

I need help finding $G_x(t)$ $f(x)= pq^{x-1}$ for x = 1, 2,... and 0 otherwise. I know $G_x(t)= M_x(ln t)$ I have started the following $$\sum_{x=1}^\infty e^{xlnt}f(x)$$ $$\sum_{x=1}^\infty ...
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3answers
37 views

Golf Question when you have uneven players teams how can you make it simple and fair

We have various sizes groups sometimes they are even sometimes not. Most of the time we have foursomes equal groups sometimes we might have 3 foursomes one threesomes. We play golf we come into the ...
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3answers
27 views

Probability picking colored stones that match a series on a card.

I'm inventing a board game that requires a person to randomly pick 4 colored gems out of a bag and have them match colored gems on a card. If I use ten each of four different colored gems, would ...
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2answers
20 views

How to calculate multiplication of probabilities when range is given?

Assume that probability of $A$ is $0.6$ and probability of $B$ is at least $0.75$. Then how do I calculate the probability of both $A$ and $B$ happening together?
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0answers
13 views

Probability of visiting each cell of an $N\times M$ grid

Consider an N by M grid. Rows are numbered $1$ to N, from top to bottom. Columns are numbered $1$ to M, from left to right. We are initially at cell $(1, 1)$ and want to go to cell (N, M). From any ...
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1answer
35 views

Arranging Couples

4 married couples entering a restaurant, there is only one table available, therefore the waiter put 4 people randomly near table and the 4 others near the bar, what is the probability that: ...
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0answers
9 views

Probabilistic Modelling of uncertain positions of objects in a 2D-Grid

I have a 2D-Grid which is populated by obstacles of different sizes. A size is always a whole number of cells. An obstacle is at least one cell big. If I did kown the size of the object but had only ...
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2answers
22 views

How to calculate the joint probability from two normal distributions

I have two random variables $X$ and $Y$ both normally distributed as $N(\mu, \sigma^2)$ (they have the same distribution). $X$ and $Y$ are dependent. They are defined from other random variables A, B ...
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2answers
31 views

Ordering Books On a Shelf

The are 6 different finance books and 4 different math books, there were arranged randomly, what is the probability that books from the same subject are standing one by the other. The answer is ...
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0answers
8 views

Simpler proof of Karp's Theorem for probabilistic recurrence relations?

A probabilistic recurrence relation is of the form $T(x) = a(x) + T(h(x))$ with $a(x)$ deterministic (usually $a(x) = 1$) and $h(x)$ being a random variable over $[0,x]$, so that $T(x)$ itself is a ...
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0answers
14 views

How to reduce the standard deviation from $P$ where $P$ involves a random integer uniformly distributed in $\left[ 0,100\right]$

I have a probability $P$ derived from: - A random integer $A$ uniformly distributed on its range such that $A\in\left[0, 100\right]$ - An integer $K$ such that $K\in\Bbb N$ - A number $X$ such that ...
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2answers
240 views

Probability- Guessing names of people

In the newspaper "Pop World," an old photo of well-known pop singers was published from when they were kids. The names of the singers are known, and one needs to identify the singers. If the ...
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0answers
6 views

Condition on Poisson random measure

It is well-known that given a $\sigma$-finite measure on a measurable space, there exists a Poisson random measure. I approach some proofs, but I want to know that if the condition of separable is ...
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1answer
17 views

Characteristic function of a non-negative random variable?

Is it possible to decide if a random variable is non-negative almost surely, by looking at the characteristic function of the random variable?
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0answers
18 views

distance distribution in Poisson point process

Consider a homogeneous Poisson point process in 2D space with density $\lambda$ per unit area. Let $\mathcal{B}(o,R)$ denote a disk centered at origin with radius $R$. Let $n$ be the number of points ...
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1answer
29 views

What are conditions under which convergence in quadratic mean implies convergence in almost sure sense?

What are the conditions on the sequence on $\{X_n\}$ (apart from the degenerate random variable), under which it can be claim that $||X_n-X||_{L^2(\mathbb{R})}\rightarrow 0$ implies $X_n\rightarrow ...
3
votes
1answer
85 views

Expected value when die is rolled $N$ times

Suppose we have a die with $K$ faces with numbers from 1 to $K$ written on it, and integers $L$ and $F$ ($0 < L \leq K$). We roll it $N$ times. Let $a_i$ be the number of times (out of the $N$ ...
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0answers
35 views

What are the main kinds of mathematics? [on hold]

I stumble upon as much on math I don't know (trascendal math, number theory) and math I know on the internet and elsewhere. I have a pretty good idea about differential and integral calculus, and I'd ...