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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0answers
15 views

Expected value (mean) of function from polyline

Suppose we have a polyline that has such properties: It consists of n segments First segment's ends are (0, 0) and ...
0
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0answers
34 views

A question of odds

Consider an experiment with four possible outcomes, and suppose that the quoted odds for the first three of these outcomes are as follows. What must be the odds against outcome 4 if ...
0
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2answers
33 views

Calculating a characteristic function two different ways gives contradictory results. Why?

I am trying to calculate a characteristic function directly and via the conditional distributions. I get contradictory results: Let $X$ and $Y$ be random variables defined on the same probability ...
0
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1answer
22 views

Probability for rolling an odd number and tossing a coin on heads

A coin is tossed and a die rolled. Find the probability of getting a head and an odd number. The answer is $\frac{1}{4}$. My reasoning is that rolling an odd number is $\frac{1}{2}$, and tossing a ...
0
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2answers
19 views

how do they calculate these following columns

I have these data: I am sorry the data is in Portuguese, and it is an image so I can't convert it to a table but the translate "probably" ( i am not a native speakers for Portuguese language) is: ...
0
votes
1answer
10 views

Cumulant-Legendre

I have a short question: So suppose $b=\text{ess sup} X<\infty$, where $X$ is a random variable on $\mathbb{R}$. Now take $\Lambda (u)=\ln \mathbb{E}[e^{uX}]$, the cumulant, and ...
2
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4answers
74 views

A combinatorial proof for $\binom mk$+$\binom m{k-1}$=$\binom {m+1}k$

I do realize that there is a elementary proof of this result which follows from applying the formula $$\binom mk=\frac{m \cdot (m-1) \cdot \ldots \cdot (m-k+1)}{k!}.$$ I do wonder if there is an ...
1
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1answer
18 views

Conditional probability of a zero inner product

Consider a random $n$ by $n$ matrix $M$ chosen uniformly over all $n$ by $n$ $(0,1)$ matrices and a random vector $v \in \{-1,0,1\}^n$ chosen uniformly as well. Let $X = Mv$. What is $$P(X_i = 0 ...
0
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0answers
14 views

Can anyone shed some light on the random variable which has the following characteristic function?

I have a random variable whose characteristic function is of the form \begin{equation} \mathbb{E}[e^{itX}] = \frac{(1-it)^a}{(1-2it)^{\frac{a}{2}}}\,, \end{equation} where $0<a<1$ I am not ...
0
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0answers
18 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 ...
0
votes
1answer
12 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 ...
1
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1answer
20 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 $b_j$. ...
0
votes
2answers
35 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) ...
0
votes
1answer
32 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 ...
0
votes
1answer
16 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
votes
2answers
36 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 ...
1
vote
1answer
29 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 ...
0
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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 ...
1
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3answers
38 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
vote
1answer
19 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
45 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
52 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.
0
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1answer
44 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 ...
1
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3answers
34 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 ...
0
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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 ...
0
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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 ...
1
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4answers
54 views

Probability question involving infinite number of vertical chords in a 1 inch circle. [on hold]

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
votes
0answers
7 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
votes
1answer
33 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? ...
0
votes
1answer
43 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 ...
2
votes
3answers
193 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 beginning to drive me nuts. The question: A man has $7$ ...
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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 $\sigma =1$ ...
0
votes
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
vote
2answers
37 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: ...
0
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0answers
15 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 ...
1
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3answers
51 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
votes
2answers
36 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
votes
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 ...
0
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3answers
38 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 ...
2
votes
3answers
29 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 ...
0
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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?
0
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0answers
14 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 ...
0
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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: ...
0
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0answers
10 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 ...
0
votes
2answers
23 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 ...
0
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0answers
9 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 ...
0
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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 ...