# Questions tagged [probability]

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

7,202 questions
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### How to find CDF of a function of continuous joint distribution from PDF of joint distribution?

Here's what I think I should proceed: Make a level curve for the function keeping the constraints given in the PDF of joint distribution in mind. Find the area of interest keeping the constraints ...
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### Favorite sequence in 10 flip tosses

I have the following question. Somebody likes to flip coins. In particular, this person is delighted to get a sequence HTTH. Assuming the person flipped coins 10 times, what is the probability that ...
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### Intuition behind product distribution pdf

Say we have two distributions $X$ and $Y$. I know that the pdf of the distribution $Z = X + Y$ is given by: $f_Z(z) = \int_{-\infty}^{\infty}f_X(x)f_Y(z-x)dx$ The intuition is that you sum up the ...
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### cannot prove simple conditional probability

Is the next true? If so, why? P(A∩B|C) = P(A|B∩C) x P(B|C) I saw as part of solution of an exercise, but I can't prove that is true, how is it possible to arrive to that?
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### Level curves and functions of pair of Random Variables?

I came across the following question: I tried solving it, the following is my 1st attempt:(2nd method at the end) 𝑃[𝑊≤𝑤]=𝑃[𝑋𝑌≤𝑤]=𝑃[𝑌≤𝑤/𝑋] And then I simply double integrated keeping the ...
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### Probability of normal random variable yielding highest value among other normal variables

Let's say I have a competition with $N$ participants. Each participant yields a score that is normality distributed with unique means and unique variations. Each participant gets to post one score (we ...
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### Expectation Maximization for a 2D Normal Model

I'm working through an example in Richard Duda's Pattern Classification on Expecation Maximization Algorithm. Specifically I'm trying to understand the expectation part, and how the parameters get ...
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### How do I reconcile the output of a decision tree visual vs the output of the DecisionTreeClassifier class?

I have a decision tree model stored in dt. I also plotted and can visually see the decision tree itself. Given a new, unseen customer, I can use the visual tree to ...
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### Calculate probability based on part of features

I have a knowledge base, where each row represent a class and columns represent features of classes: ...
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### Alternative to Hoeffding Bound in Streaming for Normally Distributed Variable?

I am reading a paper (Hellinger Distance Trees for Imbalanced Streams by R. J. Lyon, J. M. Brooke, J. D. Knowles, B. W. Stappers) on using the Hellinger Distance for Very Fast Decision Tree (VFDT)...
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### How to simulate, if a customer will buy

If customer 1 will buy a product with a probability of 0.6 and every following customer 0.7, how can I simulate a system with n customers? The result should show which customers bought and which ...
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### How to figure out whether a coin is “weighted” with some number of flips

Suppose there's a weighted coin. That coin either lands on heads every 1/10 times it is tossed, or it never lands on heads at all. I don't know whether that coin is the type of coin that lands on ...
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### How to calculate coverage probability in R for cauchy distribution?

I know that the coverage probability is $P(|\hat{\theta}-\theta|\leq\epsilon)$. My task is to compare estimators of the Cauchy distribution for the location $\theta$. I've plotted the estimators and ...
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### Addition of Gaussian with Gaussian [duplicate]

Hi I have following equations, where $T_1$,$T_2$ and $T_3$ are distributed as Gaussian.I want to know their mean and Variance. finally, I want to add them. How can I do that? All variables are ...
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### Probability of a positive outcome from 2 events that have a 2% chance of a positive outcome

Apologies for my lack of maths jargon and terminology. This seems like a very simple problem to solve. I need a formula to determine the following; If event A has a 2% chance of success If ...
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### How to estimate the mean and variance of a Gaussian distribution variable? [on hold]

I have two variables 2X and 0.5Y, both are independent and follows Gaussian distribution. How to estimate their mean and variance analytically? I want to know their individual mean and variance, then ...
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### How is $s^k$ in p.g.f. likened to Dirac measure $\delta_k$?

How is $s^k$ (sometimes $z^k$, $\theta^k$) in probability generating function likened to Dirac measure $\delta_k$? I don't see how these are similar. Yet I see them equated. Clearly the Dirac ...
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### Is this a t-distribution problem?

The problem says that the probability of student failure is 0.4 A random sample of size 10 is taken from this population. I'm asked to find the probability that, at most, 30 % of students failed. I ...
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### Markov chain questions [closed]

please answer 2, 3, 4, 5, 6, 7 please answer no. 2, 3, 4, 5, 6, 7 questions
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### What is the probability that two samples from a source have no overlap?

I picked 29 results from a list of 429 results. I then picked a second group of 27 (with replacement) results from the same list of 429. There was no overlap between the two samples. What is the ...
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### Distribution of Maximum Likelihood Estimator

Why is the Maximum Likelihood Estimator Normally distributed? I can't figure out why it is true for large n in general. My attempt (for single parameter) Let $L(\theta)$ be the maximum likelihood ...
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### Clarification on the concept of “General formulation of the problem of statistical inference” - Wald

I'm looking for clarification on one part of this definition, but also some feedback on my interpretation of the whole concept. The definition comes from the end of the first chapter of On the ...