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Questions tagged [probability]

For basic questions about probability and for questions about calculating a probability, expected value, variance, standard deviation, or similar quantity. 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.

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18 views

what is the probability that in the second box we have 2 red balls? [closed]

We have two boxes. In the first box, there are one red and one white ball. In the second box, there are either one red and one white ball or two red balls. We take out one ball from each box at the ...
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1answer
19 views

The probability that $3$ organizers win

A local fraternity is conducting a raffle where $55$ tickets are to be sold - one per customer. There are $3$ prizes to be awarded. If the $4$ organizers of the raffle each buy one ticket, what are ...
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0answers
25 views

Identify which normal distribution generated a given sample

I have $d$ Normal Distributions, $N_1(\mu_1, \sigma_1^2) \cdots N_d(\mu_d, \sigma_d^2)$. We pick one of the $d$ distributions with each distribution having a probability of $\frac{1}{d}$ of being ...
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0answers
38 views

Using Excel to Solve a Statistics and Probability Delivery Driver Problem [closed]

Frankie has heard his delivery drivers complain that they don’t have enough time to complete their scheduled deliveries, and he observed that it has been a while since he hired a new driver. The ...
1
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1answer
29 views

Bound on tail probability with knowledge of a bound on expected value

I'm trying to solve the following problem: If the random variables $X$, $Y$ satisfy: $$E[(X-a)_+]\leq E[(Y-a)_+],\qquad \forall a\in R$$ and $\forall t>0$ we have: $$P[Y\geq t]\leq ke^{-bt},\...
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0answers
22 views

Mathematical Foundations of Quantitative Finance [closed]

I really need help. I want to study an MSc in Finance but my maths has never been that good. I have got a 2:1 in business accounting but this is a new level of maths and would be grateful for some ...
5
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1answer
100 views
+50

Minimal example of Simpson's paradox

Let's say that a finite probability space $(\Omega,\mathscr P(\Omega),P)$ has Simpson's property if you can find events $A,B,C\in\mathscr P(\Omega)$ such that $P(C) \in (0,1)$. $A$ and $B$ are ...
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0answers
14 views

Representation of Generalized Quadratic Form of Random Variables

I am interested in finding/understanding a "good" $L^2$-orthogonal (i.e. uncorrelated) decomposition of a matrix-valued quadratic form. The setup is as follows: Given a random matrix $X$ (tall, of ...
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1answer
35 views

Complement of an event

What's the complement of the event $A$={not getting the number six when rolling a die 7 times}and why? The complement is not (A). I'd say $A^c$= {getting the number six(only once) when rolling a die ...
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1answer
33 views

Geometric distribution/ Formula

I have a geometrically distributed random variable $X$. I want to calculate $P(X \geq k)$. I get that $P(X \geq k)= (1-p)^{k-1}$. Now I want to show that $P(X \geq k+n \mid X\geq n) = P(X \geq k)$. ...
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0answers
15 views

Probability of n failures with possibility of machine breakdown

I am having a problem with the following question. Consider a machine which at each time step involves two random processes. First, with probability $1-a$, the machine breaks down. If it breaks down, ...
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0answers
22 views

Sum of two dependent random variables with copula

I'm trying to calculate the sum of two random variables by using Copula Theory in R or Matlab. However, I have very limited knowledge about probability. Actually I read a lot of theoretical ...
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1answer
24 views

Probability of hitting a specific number out of 100 with a dice roll of 12

I’m trying to figure what the probability of hitting a number I pick out of 100 with a dice roll of 12. I’m familiar with the equation of rolling a specific number in a certain amount of rolls but, I ...
1
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1answer
33 views

Expected amount of tries to be made until success

lets say I have something (guessing a byte) that occurs with the probability of $\frac{1}{2^8}$. So when I guess once, the probability of me guesing the byte right is $\frac{1}{2^8}$. I know that I ...
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4answers
45 views

Choice between element

Let's say we have a fair coin. We have $1 \dots n$ different Elements. We want to select one of these n elements with the coin. Each element should have the same chance to be selected. In addition, ...
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0answers
22 views

Need the Formula to calculate odds of losing

I enter a raffle every week. I have 1 out of 18 chances to win. Each, obviously, is independent of the previous. I have not won in the last 100 drawing. What are the odds of that? What's the ...
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0answers
27 views

Get some statistics from a dataset [closed]

I have list of prices for some stock. The price might change within a month, I have list of averages for each month and list of min prices for each month(something like this, but more data): ...
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1answer
13 views

Prove that a random variable defined in terms of lim sup of independent random variables is constant

I'm asked to do the following: Let $(X_n)$ be a sequence of independent random variables. Show that the following random variable is constant almost surely: $$X = \begin{cases}\exp\{-\limsup_{n \to \...
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0answers
21 views

Maximize expected utility of reward [closed]

This task is given from DeGroot Optimal Statistical decisions book.
5
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0answers
41 views

Necklace is made out of ten different red, twenty different orange and thirty same yellow pearls.

Necklace is made out of $10$ different red, $20$ different orange and $30$ same yellow pearls. If we know that no two red pearls are next to each other, what is the probability of the case where ...
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1answer
25 views

Probability regarding computer science

Consider the following program segment: if B then repeat S1 until B1 else ...
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0answers
21 views

Hypergeometric Probability - Average chances after multiple trials

Hopefully someone can help me out here. I'm stuck on a few hypergeometric probability calculations I'm working on for an assignment. I'm stuck on finding the average chances from Trial 3 and onwards. ...
1
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1answer
42 views

Discrete mathematics: chances of getting specific card on card-game

The game is played with a deck of $40$ cards. Three of them are dealt to each of two players, so my hand, the cards that were given to me, is formed by three cards of the deck. At the same time, ...
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0answers
9 views

trying to figure out the pvalue if I know the significant level of 0.10 the critical values of -1.935 and 1.935 and degrees of freedom is 14 [closed]

trying to figure out the P-value if I know my significant level of 0.10 and critical values of -1.935 and 1.935 and degree of freedom is 14. My calculator is broke .
1
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1answer
20 views

How many ways are there to arrange three groups of people around a circular table?

I have the following question: Three Koreans, three New Zealanders and three people from Bosnia are seated at random around a round table. What is the probability that the people in the three groups ...
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0answers
32 views

A jar contains $2$ pennies, $6$ nickels and $4$ dimes. A child selects $2$ coins at random without replacement from the jar. [closed]

A jar contains $2$ pennies, $6$ nickels and $4$ dimes. A child selects $2$ coins at random without replacement from the jar. Let $X$ represent the amount in cents of the selected coins. a. Find the ...
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0answers
48 views

A variant of the boy/girl paradox

Some friends and I were arguing about the two following word problems, which are variants of the classic boy/girl paradox. (i) "Mrs.Smith lives in a world where the eldest child is always male. She ...
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0answers
26 views

Gambler´s ruin for a Binomial multiplicative process

I would like to calculate the gambler´s ruin probability in a generalization of the classic gambler´s ruin problem. In the classical model, the gambler´s wealth could be modeled by an additive random ...
0
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0answers
8 views

Entropy of a race and information of a message [duplicate]

Having 17 people running a race, the 1st runner have 3/4 probability of winning and all the others have (each) 1/64. The entropy of the marathon is 1.811bits.Knowing that the 1st runner didn't won ...
0
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1answer
25 views

Markov Chain involving gerrymandering in Pennsylvania.

I am currently working on a project that involves the use of analyzing the 18 districts of Pennsylvania and using the results of the 2018 house of reps congressional election. I understand that ...
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1answer
30 views

Probability density of the product of independent identically distributed random variables

Let $X_1, X_2, \dots , X_n$ be a random sample from the PDF $$f(x;\theta)=\theta x^{\theta -1},\;\; 0<x<1,\;\; \theta > 0$$ What is the probabilty that $\prod_{i=1}^n X_i > t$? The joint ...
2
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1answer
61 views

Minimise a function of 3 variables.

If I have a function of 3 positive variables, $k$, $m$ and $n$, how can I find what value of $k$ minimises this function (in terms of $m$ and $n$)? The particular function I'm interested in is this: ...
2
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1answer
48 views

If $E[X|Y= y] = y^2$ for all $y$, does it follow that $E[X| Y] = Y^2$?

Let $X,Y: \Omega \to \mathbb{R}$ be two discrete random variables on a probability space $(\Omega, \mathcal{F}, \mathbb{P})$, and $\mathbb{E}[|X|]< \infty$. Suppose that $\mathbb{E}[X|Y=y] = y^2$ ...
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1answer
24 views

What is the distribution of a nested Laplace?

We have three random variables $X_1, X_2, X_3$ having the following conditional distributions: \begin{align} p(X_2 \mid X_1=x_1) &\sim \mathrm{Laplace}(X_2;x_1, b) = \frac{1}{2b} \exp(-\frac{|X_2 ...
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1answer
38 views

Expectation of a hitting time

I'm trying to find the expectation of a stopping time. Specifically, Let $T_1,...,T_n$ be i.i.d exponential random variables with mean $1$. Let $S_n = T_1 + ... + T_n$ denote their partial sum. ...
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1answer
33 views

Inequality involving log-sum-exp, variance, and mean

Fix $z_1,\ldots,z_n \in \mathbb R$. Let $\mu_n:= mean(z_1,\ldots,z_n):=\frac{1}{n}\sum_{i=1}^n z_i$, $lse_n(z_1,\ldots,z_n)=\log(\sum_{i=1}^n e^{z_i})$, and $\sigma^2_n := variance(z_1,\ldots,z_n):=\...
5
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1answer
43 views

Picking $6$ numbers from $\{1, \ldots, 49\}$, what is the chance that the difference between at least $2$ of them is $= 1$?

You choose $6$ different natural numbers from $\{1, \ldots, 49\}$. What is the probability that at least $2$ of these numbers have a difference equal to $1$? E.g. $1, 2, 10, 20, 30, 31$ - you'd ...
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0answers
36 views

Probability of identical test answers [closed]

What is the probability of two students getting identical answers on a 50 question multiple choice test with each question having four answers choices. Both of them got an 85% (42.5/50) with the class ...
1
vote
1answer
49 views

Proof with the expected value [on hold]

I wonder if the following statement is true: Assuming that $X>Y$ with probability 1, show that $$ E|X-Y| = E(X-Y) = EX - EY. $$ Intuitively I think it is correct, however I need a formal proof.
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0answers
39 views

evaluate conditional probability in brownian motion

Let $W_t$ be a standard brownian motion, and let $0 < x < y$. We want to calculate: $\mathbb{P}(W_y > 0 \vert W_x > 0)$. I am pretty stuck on how to do this. The only insight I have is ...
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0answers
30 views

Gambler's ruin vs point difference

Two people want to investigate who is best at playing Scrabble. They decide to settle this by playing a series of games. Assume that there is always a winner for each game, and that winning or losing ...
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2answers
19 views

How many different words can be formed in which neither two consonants nor two vowels can come next to each other? [on hold]

There are 6 letters of which 3 are consonant and 3 are vowels. How many different words can be formed in which neither two consonants nor two vowels can come next to each other?
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1answer
14 views

How to solve for the values of variables to give the maximum probability of an outcome

A small boy is lost coming down Mount Washington. The leader of the search team estimates that there is a probability p that he came down on the east side and a probability 1 - p that he came down on ...
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1answer
17 views

How do use inclusion-exclusion to find the probability of encountering all n outcomes in m tries

This is a repost as my last post broke some rules. Assume that every time you buy a box of Wheaties, you receive one of the pictures of the n players on the New York Yankees. Over a period of ...
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1answer
25 views

lim sup of i.i.d. random variables in terms of their distribution function

Let $(X_n)$ be i.i.d. with distribution function $F$. I'm asked to prove that $$\limsup_{n \to \infty} X_n = M \text{ almost surely}$$ where $M = \inf\{t \in \mathbb R : F(t) = 1\}$. My approach ...
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1answer
47 views

Can you please tell me which formula this is?

I am working on a recommendation system, which uses the euclidean distance formula to calculate the similarity between 2 users. Euclidean distance Thereafter, it uses a formula to predict the rating ...
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votes
0answers
32 views

Probability of getting identical answers on multiple choice test [closed]

What is the probability of two people getting identical answers on a multiple choice test with 4 answers. Lets say they both got an 85% and the average was 85%. Are they cheating?
0
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1answer
44 views

You are flipping n fair coins, putting aside those that come up heads after each flip. What's the expected number of rounds?

This question is related to https://www.quora.com/You-are-flipping-100-coins-putting-aside-those-that-come-up-heads-after-each-flip-How-many-flips-do-you-expect-to-make-before-running-out-of-coins-to-...
0
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1answer
21 views

Conditional expectation in the discrete case

Let $X: \Omega \to \mathbb{R}$ be a random variable with $\mathbb{E}[|X|]< \infty$, and suppose that $Y: \Omega \to \mathbb{R}^d$ is a discrete random vector. Define $$f(y) = \begin{cases}\frac{1}{...
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votes
2answers
28 views

Random variable and probability calculations

X is a random variable that follows a binomial property, with E(X) = 36 and $\sigma$(X) = 3. Calculate p(X = $10$) I know that the variance is V(X) = 9 and I know that I have to use the formulas of ...