Questions tagged [probability]

A probability provides a quantitative description of the likely occurrence of a particular event.

Filter by
Sorted by
Tagged with
0 votes
0 answers
15 views

Determines the probability that a specific order of repair will be chosen

Consider the statement In an appliance repair shop, the following are found $10$ televisions for repair, of which $3$ are of brand $A$, $3$ of brand $B$ and $4$ of brand $C$. The order in which the ...
Wrloord's user avatar
  • 135
1 vote
0 answers
15 views

Do operator on a 2 node system

If my causal structure consists of $y$ influencing $x$ (so the DAG would simply be $y\to x$), my understanding is that $p(x|do(y=1))=p(x|y=1)$. But what is wrong with the following argument? $$p(x|do(...
theQman's user avatar
  • 677
1 vote
0 answers
62 views

The expected value and variance for the sum of 4 dice rolls only if a coin gives Head

Edited: toss a fair coin 4 times and then roll a fair 6-side dice whenever the coin gives a head H. Let X be the sum of the dice rolls. How to calculate E[X] and <...
Sandra Sukarieh's user avatar
8 votes
2 answers
509 views

Is the realization of random variable also a random variable?

In class, a teacher told me that the realization of a random variable is also a random variable. For example, if I take the a sample mean, and that mean results in the value 35, then 35 is also a ...
Santiago Valdivieso's user avatar
1 vote
0 answers
34 views

Finding probability involving dependent random variables [closed]

Suppose train on line A arrives in time uniformly distributed between 0 and 4mins, train on line B arrives in time uniformly distributed between 0 and 6 mins, and furthermore the time interval between ...
Harsh's user avatar
  • 11
0 votes
1 answer
36 views

Sampling from multivariate probability distribution

What's the best way to sample from multivariate probability density functions that are proportional to $\exp(-\|x\|_2)$ or $\|x\|_2^p \exp(-\|x\|_2)$ for some positive integer $p$ with $x \in \mathbb{...
user808843's user avatar
1 vote
0 answers
22 views

Switching from General to Specific in Maximum Likelihood Estimation: Why Use $y_i$​ Instead of $a$?

I've been working through a statistical model that utilizes both the cumulative distribution function (CDF) and the probability density function (PDF) to describe the behavior of a variable $y_i$ ...
Littlegiant's user avatar
2 votes
2 answers
82 views

Find $P(Y>\frac{5}{4})$ when joint pdf of $X$ and $Y$ is given

The joint pdf of $X$ and $Y$ is given as $f(x,y)$ = $\frac{1}{2x^2y}$ , $1<x<∞$ and $\frac{1}{x}<y<x$ Then find $P(Y>\frac{5}{4})$ Since the limits of $Y$ have $X$ in them, I am not ...
Anweshan Goswami's user avatar
2 votes
0 answers
39 views

Distribution IID uniform variables given their ranking [duplicate]

Description Let $N\in\mathbb{N}^{+}$ and $X_{n}\stackrel{IID}{\sim}U(0,1)$ for $n\in\{1,...,N\}$. Given $X_{1}\leq X_{2}\leq X_{3}\leq...\leq X_{N}$, I would like to understand $f_{X_{n}}$ by writing ...
CorrieElba's user avatar
2 votes
0 answers
38 views

Maximum Mean Discrepancy (MMD) implementation as a metric to measure GAN performance

I am trying to evaluate the performance of the GAN model, I have trained. I found that there exist two major choices FID (Fréchet inception distance) and MMD (Maximum Mean Discrepancy) for comparing ...
Rajesh Nakka's user avatar
-2 votes
0 answers
73 views

Fallacy of composition in longitudinal research [closed]

Consider the claim that IQ is stable over the lifespan. Individuals at the lower end of the spectrum dies - 10 or 20% of the population dies young over the term of a lifespan study from childhood to ...
Syys Sus6s7's user avatar
0 votes
0 answers
42 views

Does central limit theorem apply to the following product case?

All! I know the central limit theorem works for a lot of cases, and some variants including Lindeberg are also pretty useful, but now I met such product case, and wondering if some classical or ...
0o0o0o0's user avatar
  • 21
7 votes
3 answers
394 views

How do I compute a probability from the MGF?

I have a random variable $X$ with moment generating function: $$m_X(t) = \frac{2}{9} + \frac{e^{-t}}{9} + \frac{e^{-2t}}{9} + \frac{2e^{t}}{9} + \frac{e^{2t}}{3}.$$ I want to find the probability $\...
Anweshan Goswami's user avatar
0 votes
0 answers
17 views

Difference Between Conditional Distribution and Distribution Parameters

Is there any connection between the parameter of a probability distribution and a conditional distribution? What I am wondering about is, whether or not there is some notational shorthand or implicit ...
BurgerMan's user avatar
0 votes
0 answers
31 views

Probability of a certain final score in soccer when you know each of the two teams' probabilities to score a certain number of goals

Let's suppose that you have data from about $2000$ soccer matches from a certain league. Your data shows that the home team's probability of scoring $0$ goals is $0.245263157894737$. The away team's ...
Giorgos Papatheodorou's user avatar
1 vote
1 answer
45 views

Number of simulated statistics more extreme than most extreme real data statistic

I have a distribution of $n_{obs}$ "real" data observations drawn from a normal distribution $X \sim N(\mu,\sigma^2)$, and a number $Q$ of simulated realizations of the same distribution, ...
user406833's user avatar
0 votes
0 answers
10 views

Estimating a subpopulation's size based on distribution

Say I have population $ n_1{} $, where each individual samples is unique and contains multiple traits. A subset of population$ n_1{} $ forms a population that I'm interested in, called $ n_2{} $. Each ...
Bert's user avatar
  • 1
0 votes
0 answers
10 views

How do you get joint probability of two events conditional on the same event? [migrated]

I want to get the joint probability of two independent events, both conditional on another event. What I know: Probability of A is 0.2375. Probability of B given A is .8. Probability of C given A is ....
Andrew Button's user avatar
0 votes
1 answer
39 views

Optimization of fault diagnosis sequence using probability and cost [closed]

I am developping the algorithm to optimize the fault diagnosis sequence using probability and cost. For exemple, I have 3 diagnosis actions possibles : option 1 : probability which can detect the root ...
stat_man's user avatar
0 votes
1 answer
40 views

Probability to get a 1 in 5 rolls 3 or more times

If I roll a dice 5 times, what is the probability to get 3 or more ones? That is, to roll a one three or more times? Because I think it's near 0.05: $ \binom{5}{3} \left(\frac{1}{6}\right)^3 = 0.046 $ ...
robertspierre's user avatar
11 votes
2 answers
2k views

A and B are independent. Does P(A ∩ B|C) = P(A|C) · P(B|C) hold?

Let $C$, $B$, and $A$ be events in the same probability space, such that $A$ and $B$ are independent and $P(A \cap C) > 0$, $P(B \cap C) > 0$. Prove or disprove: $P(A \cap B|C) = P(A|C)P(B|C).$
user406596's user avatar
0 votes
1 answer
76 views

Variance of Multimodal Generalized von Mises Distribution?

How do you calculate the variance of a Multimodal Generalized von Mises (MGvM) distribution? Given its complexity with multiple modes and asymmetry, I'm looking for: Any formula or method to calculate ...
Alireza Ghazavi's user avatar
3 votes
2 answers
183 views

Calculating $E[(\sum X_i)^4]$

Trying to figure where I'm going wrong with the following. My goal is to calculate var$(\bar X_n^2)$ using $E[(\bar X_n)^4]=\frac{1}{n^4}E[(\sum X_i)^4]$ given that $X_1,...X_n$ are iid with $EX_1=\mu,...
reyna's user avatar
  • 353
0 votes
0 answers
21 views

Guessing the size of a set based on number of repeated random draws

I am trying to study a problem in algebraic number theory through a set of computational experiments. I have an enormous (say, of size $X$) family $\mathcal{F}$ of polynomials and I'm trying to ...
davidlowryduda's user avatar
1 vote
1 answer
63 views

If $X \sim\textrm{ Bin}(100, 0.5), $ then what is the approximate distribution of $(X/5 - 10)^2? $

I am not able to solve this using transformation since binomial does not have a CDF. The question has 4 options, so I tried calculating the expectation of this and then comparing it to the ...
Anweshan Goswami's user avatar
0 votes
1 answer
48 views

Why is pnorm giving different results with X, sd and mean vs corresponding z value?

I have to calculate $P(X < 6)$ for $X \sim N(7,5)$. When I entered pnorm(6, mean=7, sd=5) into R, it gave me a result of <...
Peter Ambos's user avatar
3 votes
1 answer
69 views

Can we write $\int_p^\infty\int_q^\infty f(x,y)dxdy=\int_p^\infty\int_q^\infty\frac{\partial^2}{\partial x\partial y}F(x,y)=F(\infty,\infty)-F(p,q)$?

Let $(X,Y)$ be non-negative absolutely continuous random vector with density function $f(x,y)$ and distribution function $F(x,y)$ and $\frac{\partial^2}{\partial x\partial y}F(x,y)=f(x,y).$ Can we ...
Unknown's user avatar
  • 163
2 votes
1 answer
103 views

Error rate vs Empirical risk - What's the difference between practical and theoretical terms for performance of neural networks?

Motivation I am currently reading the following book: Understanding machine learning by Shalev-Shwartz and Ben-David. The book uses statistics terminology in its machine learning theory, and it is not ...
Mr. Fox's user avatar
  • 21
3 votes
1 answer
69 views

How to incorporate prior knowledge after ML training?

Assuming I have trained my ML classifier on a balanced dataset with 5 classes. The model performs well with training and test data. The model's predicted confidence lines up well with the probability, ...
YPOC's user avatar
  • 155
2 votes
1 answer
56 views

Can a ML classifier's prediction be understood as a probability?

When predicting classes with a machine learning classifier, such as scikit-learn's DecisionTreeClassifier or KNeighborsClassifier...
YPOC's user avatar
  • 155
0 votes
1 answer
33 views

How many A is needed to be B number of results with a C probability?

I am able to perform action XYZ once a week. The success rate of action XYZ is 15%. If I want XYZ to exceed 5 times, what is the expected number of weeks it'll take?
Tyler Hilbert's user avatar
1 vote
0 answers
78 views

What might be causing equal variances all over the predictions? (GP / BO) [closed]

I have 1D data here. I create labels with a comparison of consecutive pairs. I use the value gamma to decide the label. If data at row x is gamma much bigger than data at row x+1, the label is -1. If ...
user avatar
0 votes
0 answers
30 views

Mutual information with convex combination of dependent variable and random noise

Suppose I have random variables $A, B, C$ where $B$ is statistically-independent of $A$ and $C$ (e.g. it is random noise). Consider scalars $0 < \alpha < \beta < 1$ and random variables $X = (...
Jimmy's user avatar
  • 1
0 votes
0 answers
32 views

A recurrent Markov Chain implies its k-step version is also recurrent?

I am curious about whether a Markov Chain $X_n$ is recurrent implies that for any $k > 0$, $X_{kn}$ is also recurrent. Here are my observations. If $X_n$ is transient, $X_{kn}$ must be transient by ...
qqhgsjah8221's user avatar
-2 votes
0 answers
34 views

A question on probability distribution independence: PT: $A\perp(Y,R) \land A\perp R \implies A \perp Y$

I need to prove that $$A\perp(Y,R) \land A\perp R \implies A \perp Y$$ I am right now using the following approach which seems incorrect to me. We are given the following: $P(A,Y,R) = P(A)P(Y,R)$ and $...
A J's user avatar
  • 25
0 votes
0 answers
18 views

Correct way to compute denominator in the bayes theorem

Say I have two data points and two Gaussians that these might be coming from. What is my evidence in this case? $P(X) = \prod_{i=1}^{2} (p(xi|\mu1)p(\mu1) + p(xi|\mu2)p(\mu2)) $ Because my samples ...
figs_and_nuts's user avatar
8 votes
6 answers
2k views

Infinite dice roll probability

The following is an interview question: Two players A and B play a game rolling a fair die. If A rolls a 1, they immediately reroll, and if the reroll is less than 4 then A wins. Otherwise, B rolls. ...
Ria's user avatar
  • 501
0 votes
0 answers
53 views

Urn problem. How to calculate this probability?

Drawing n times from an urn that has m unique elements. Drawing one at a time, with replacement. What is the probability that resampling happens during a draw on average? Clarification: The first draw ...
Dav Bhaji's user avatar
2 votes
3 answers
100 views

Why do we work with factor of likelihoods instead of e.g. a sum for a batch in the negative log likelihood loss function?

In a classification task, at a certain stage of the training process, we get a likelihood of sampling proper class Y for a particular data point X. For batch, we get many independent likelihoods. Let'...
Maciek Gruszczyński's user avatar
0 votes
0 answers
15 views

Sampling from large Bayesian network of particular form

I want to know whether there is an efficient way of sampling from this special kind of Bayesian networks of the following form (like thousands or millions of variables in principle). Here is a picture ...
swish's user avatar
  • 135
1 vote
1 answer
58 views

Name of PDF? - projecting uniform probability distribution on the unit circle to the x-axis

Consider a uniform probability distribution on a circle of radius r, i.e. $\{(x,y) \in \mathbb{R}^2: x^2 + y^2 = r^2 \}$.If we wish to project onto the x-axis, we can consider each point on the circle ...
SSD's user avatar
  • 185
2 votes
0 answers
53 views

Success of Bernoulli trials with different probabilities, but a probability is only changed after success

I would like to compute the Bernoulli trials with different probabilities, but the probability is only changed after success. Such as here, all probability, p, is different at each state, s, in the ...
K-John's user avatar
  • 21
-1 votes
1 answer
86 views

what is actually the difference between prior and evidence?

when saw bayes theorem prior and evidence, it has similarity to joint probability (A n B). so is there really a clear difference between them???
Kelvin Wijaya's user avatar
5 votes
1 answer
79 views

Advantages of using Vine Copulas over Regular Copulas?

I am new to Copulas and am trying to conceptually understand that differences between the two main types of Copulas: Regular Copulas and Vine Copulas. Both are used to simulate data from correlated ...
Uk rain troll's user avatar
1 vote
0 answers
23 views

How to accurately determine if a random method is indeed random? [duplicate]

I wanted to do a project where I measured how random the native RNGs are in various programming languages. How can I objectively measure my results? Also, if you run a random number generate say 100 ...
skarz's user avatar
  • 131
1 vote
0 answers
46 views

When is a function of an ergodic stationary process itself ergodic stationary?

I am working with a function which has the form $f(X_1, \dots, X_n)$, where $\\{X_n\\}$ is an ergodic stationary process. Theorem 5.6 in "A first course in stochastic processes" by Karlin &...
Kristan's user avatar
  • 11
4 votes
1 answer
201 views

Is there a mathematical function with a shape like an inverted sigmoid pdf but X values that go beyond 1?

I am looking for a mathematical function that can produce a shape like the one below: The above curve has probabilities ranging between 0 and 1, with the x values being able to take any positive ...
André.B's user avatar
  • 1,450
4 votes
3 answers
306 views

Deriving the Distribution of Markov Chain Times

I am interested in learning how to derive the probability distributions for the Time to Absorption in Markov Chains (Discrete and Continuous). In the past, I have usually done one of the following: ...
Uk rain troll's user avatar
0 votes
0 answers
20 views

Why do we add 2 to the denominator when doing laplace smoothing? [duplicate]

Every explanation of laplace smoothing for, e.g, spam filtering, includes the following: The solution is to never let any word probabilities be zero, by smoothing them upwards. Instead of starting ...
Foobar's user avatar
  • 327
1 vote
0 answers
81 views

About paper "Deep Unsupervised Learning using Nonequilibrium Thermodynamics"

Here is the paper link related to the question from my title. In Appendix B, it computes the entropy of $p(X^T)$ and says "By design, the cross entropy to $\pi(x^t)$ is constant under our ...
user405729's user avatar

1
2 3 4 5
250