# Questions tagged [probability]

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

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### Completing the square and marginalizing a multivariate Gaussian [closed]

Edit: This question has been closed for being unrelated although I see similar questions posted here with the same objective, yet not with enough detailed answers or not exactly what I am looking for (...
1 vote
30 views

### Estimating the probability of a sum of events

I have n machines that use the same utility. Each machine randomly demands a unique f_n flow rate of the utility once every h_n hours on average. Each machine's demand event lasts for about m_n ...
947 views

### Basic probability question but struggling (brain teaser with friend)

You are presented with a bag of 4 orbs. You know that 2 are blue and 2 are red. You start drawing them without replacement from the bag one-by-one. Before each draw, you are given the opportunity to ...
3k views

### How many numbers can I generate and be 90% sure that there are no duplicates?

Suppose I am generating random 4-digit numbers. Obviously there are 10,000 possible numbers, but the chances are I will get a duplicate long before I generate that many. Can anyone explain how I would ...
10 views

### Predicted Probability and Interaction Terms

This is my first time asking a question here, so apologies if I failed to include all necessary information. I have run GLMM's in the past but have limited experience with assessing interaction terms. ...
11 views

### How to calculate Revenue of combined listing

I have a 3-floor apartment with 6 bedrooms. I have listed it on Airbnb in 4 different ways: (1) Entire apartment with 6 bedrooms, and (2) Three separate listings for each floor, each with 2 bedrooms. ...
36 views

### Find the CDF of a Probability Density Function [closed]

I'm having trouble with this problem. I tried integration using -1 as the lower limit, and x as the upper limit. I got $\frac34x - \frac{x^3}3 + \frac5{12}$, but I'm getting the sense that is wrong.
12 views

### The dependency in the instances of a random variable [duplicate]

Suppose we have a list L of all root words in English numbered from 1 to n. The data is any English text (let's say a text from a book) where each word is replaced by its root. You are given the data ...
24 views

### How to compute 95% Credible Interval for a T distribution with known Mean and Variance

I have a non-central T distribution from a predictive posterior $P(x|D,\theta)=t(\mu,\tau^2,v)$ with known parameters and I want to compute the 95% credible interval of the mean prediction. I know ...
1 vote
35 views

### Conditional probabilities of a chain of variables depending on one another

Suppose there are $T$ variables $\{x_1, x_2, ..., x_T\}$, and they have the following relationship $$p(x_t|x_{t-1}) = N \big( x_t; \sqrt{1-\beta_t}x_{t-1}, \beta_tI \big)$$ that means there is a ...
1 vote
37 views

### Statistical model for likelihood that an athlete will "place" in track and field

I'm trying to come up with some sort of statistical model to predict how likely an athlete would be to place in a track and field event (e.g. 100m run) based on their time. I was thinking it would be ...
17 views

### Probability, Sum of RVs [closed]

Let X and Y be independent exponential random variables with expected values E[X] = 1/3 and E[Y ] = 1/2. Find the PDF of W = X + Y .
34 views

### Are there conditions for which the Pareto distribution arises? Are there characterization theorems of the Pareto distribution?

There are many real-world phenomena in which a variable of a population follows the Pareto distribution. I am wondering, what are the sufficient conditions for the distribution to be Pareto? And if it ...
54 views

### Simulating the outcome of X number of random trials

Let's say I want to flip a coin a billion times and count how many heads I get. But I don't have time to actually flip a coin a billion times. Assuming I have a random number generator than can ...
39 views
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### How to create optimal cut-off scores for a test placing students into different courses

Our goal is to determine optimal cut-off test scores for course placement. The course placement has already been manually assigned to each test-taker. The goal is to replace this manual labor with the ...
5 views

### If the integral of the product of t and phi(t) converges, does the random variable have continuous density? [migrated]

If $\int|t\varphi(t)|\mathrm{d}t < \infty$, where $\varphi(t)$ is the characteristic function of a random variable $X$, does $X$ have continuous density? My current thinking is: not necessarily. ...
21 views

### A simple probability model for an epidemic simulation

I'm creating a epidemic simulation program in Python, but I'm stuck trying to determine the probability of being infected (if exposed). I have an m x n grid with 0's and '1 (0's represent healty cells,...
56 views

### Bayesian Inference: Conceptual question to get evidence

currently I am trying to implement a prototype for the following problem. I have data for machines, which sends me how long they have operated in seconds. Further, they have one sensor, which might ...
1 vote
30 views

### Is there a valid way to demean a categorical variable?

I have read about use of centering an explanatory variable in regression analysis on the mean (through demeaning) when there is presence of multicollinearity. I have applied this for a binary ...
11 views

### exchangeability in LDA

Can someone help me understand how exchangeability works for Latent Dirichlet Allocation (LDA) and how it enables us to treat words in the test set that are not present in the training set? I know ...
35 views

### Probability of Event if Another Occurs

An enemy that can drop loot has a 10% probability of spawning out of all enemies. Only one model type can drop loot out of 8 models (1/8). What is the probability of a specific enemy dropping loot, if ...
35 views

### What is the intution between point estimation of model parameters in statistics?

I am reading a topic about point estimation of model parameters. I understood it as follows: We have "observed" a sample $X_1,...X_n$ where we know it's distribution, i.e. the sample is ...
30 views

### Expected Win (or Loss) of Base (Spin) Game Winning Combination and Bonus (Guess the Colour) Game

I'm trying to figure out the right way of calculating an expected win (or loss) for a single winnings combination of a slot base game spin with a bonus game (guess the colour). Let's say a player ...
32 views

### Bayesian model for the reliability of a manufacturing process with noninformative prior

We have a manufacturing process $M$ with an unknown reliability $R \in (0,1)$, and, at the end of it, an automatic tool that sorts the good and bad products with a known efficiency of $E \in (0,1)$. ...