# Tagged Questions

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

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### A Probability distribution value exceeding 1 is OK?

On the Wikipedia page about naive Bayes classifiers, there is this line: $p(\mathrm{height}|\mathrm{male}) = 1.5789$ (A probability distribution over 1 is OK. It is the area under the bell curve ...
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### How to generate correlated random numbers (given means, variances and degree of correlation)?

I'm sorry if this seems a bit too basic, but I guess I'm just looking to confirm understanding here. I get the sense I'd have to do this in two steps, and I've started trying to grok correlation ...
6answers
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### Why does a 95% CI not imply a 95% chance of containing the mean?

It seems that through various related questions here, there is consensus that the "95%" part of what we call a "95% confidence interval" refers to the fact that if we were to exactly replicate our ...
12answers
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### What is the most surprising characterization of the Gaussian (normal) distribution?

A standardized Gaussian distribution on $\mathbb{R}$ can be defined by giving explicitly its density: $$\frac{1}{\sqrt{2\pi}}e^{-x^2/2}$$ or its characteristic function. As recalled in this ...
16answers
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### What's the difference between probability and statistics?

What's the difference between probability and statistics, and why are they studied together?
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### How can I determine accuracy of past probability calculations?

I do not study statistics but engineering, but this is a statistics question, and I hope you can lead me to what I need to learn to solve this problem. I have this situation where I calculate ...
6answers
8k views

### How to easily determine the results distribution for multiple dice?

I want to calculate the probability distribution for the total of a combination of dice. I remember that the probability of is the number of combinations that total that number over the total number ...
2answers
592 views

### Meaning of probability notations $P(z;d,w)$ and $P(z|d,w)$

What is the meaning between the notation $P(z;d,w)$ and $P(z|d,w)$ which is commonly used in many books and papers?
1answer
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### How to define a distribution such that draws from it correlate with a draw from another pre-specified distribution?

How do I define the distribution of a random variable $Y$ such that a draw from $Y$ has correlation $\rho$ with $x_1$, where $x_1$ is a single draw from a distribution with cumulative distribution ...
1answer
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### Probability of getting between

...2 to 5 questions answered correctly, out of 20 of them? Each question has 5 choices. Probability of getting one right is 1/5. Probability of getting exactly 1 right is ${20 \choose 1} p^1 q^{19}$, ...
12answers
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### The Monty Hall Problem - where does our intuition fail us?

From Wikipedia : Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, ...
7answers
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### What is the probability that this person is female?

There is a person behind a curtain - I do not know whether the person is female or male. I know the person has long hair, and that 90% of all people with long hair are female I know the person has a ...
4answers
677 views

### Probability over multiple blocks of events

I'm trying to find the probability of getting 8 trials in a row correct in a block of 25 trials, you have 8 total blocks (of 25 trials) to get 8 trials correct in a row. The probability of getting any ...
3answers
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### What will be the correct answer, if we modify the “Best statistics question ever”?

There is a popular question, called "Best statistics question ever". If you choose an answer to this question at random, what is the chance you will be correct? A) 25% B) 50% C) 60% D) 25% This ...
2answers
421 views

### What is the difference between using the multiplication rule or using Venn diagram subtraction for probability?

Take two problems: Andrew is 35, and the probability he will be alive in 10 years is .72. Ellen is 35, for her, .92. Assuming these are independent, what is the probability they both will be alive ...
2answers
325 views

### What is $P(X_1>X_2 , X_1>X_3,… , X_1>X_n)$?

All $X$ are mutually independent and from normal distributions, each with its own mean and variance. If it's easier, $P(X_1 \geq X_i \forall i \in \{1, ..., n\})$ is fine although I suspect it's the ...
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1answer
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