# Questions tagged [probability]

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

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### how to multiply two conditional probabilities in general

I am trying to understand how to multiply two conditional probabilities. $P(X|C) \times P(C| P,S)$ seems to equal to $P(X,C | P,S)$. How to understand this? I understand the product rule, but how ...
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### What is the distribution of the sum of a Log-Normal variable and a Logistic variable?

I was wondering if there is any known distribution that is the sum of a Log-Normal variable and a Logistic variable is? What about the sum of Log-Logistic and Logistic? We can assume the variables ...
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### Conditional Covariance Problem

Suppose we have independent (not necessarily identical) normally distributed random variables X, Y. If we're given that, upon sampling each variable, X is some multiple a of Y (i.e. x = ay), what is ...
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### bivariate transformation when U=X/Y and Y=0

I am considering using transformation U=X/Y and V=Y (X,Y are iid distributions defined on real line). Almost all the textbooks I have read did not consider the case when Y=0, at which U is undefined. ...
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### Probability of absolute value of a sum of random variables

Consider two random variables $X$ and $Y$, and let $b$ be a real number. Show that $$P(\mid X+Y\mid>b)\leq P(\mid X+Y\mid>b,\mid X\mid>b/2)+P(\mid X+Y\mid>b,\mid Y\mid>b/2).$$ I'm ...
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### Find confidence interval of mean without knowing sample size?

In our calculation, we have only $\mu$ and $\sigma$ values. Is that possible to find the confidence interval of $\mu$ and $\sigma$, without knowing the sample size? As per our idea, we can calculated ...
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### Probability of association in logistic regression models

I’m using a logit model to evaluate the association of a set of habitats (H) to a particular land cover. Both land cover and H are binary variables. ...
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### How to derive a ranking function from observations

I have a employee dataset with the following 5 details. projects completed customer ratings number of bugs reported customer complaints profit I want to rank ...
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### Predict Taking a Loan

I want to build a Logistic Regression model to help me predict taking a loan by a customer base on several variables. I started building a data set for the customers who already took loans and some ...
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### Unusual Markov inequality for normal distribution

I'm trying to answer the following question from Larry Wassermans book on statistical inference. My question is how did they arrive at the Markov bound, it does not seem like the normal form of the ...
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### survival probability to proportional hazard ratios in r

I am using Cox proportional hazard regression to determine the association between physical behaviors (physical activity, sedentary behavior, and sleep) and mortality. to elaborate on these results, I ...
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### Bayesian chi-squared tests

I have a dataset with two groups of participants. Each participant performed a repeated measures task on which three types of errors could be made. I want to measure the difference in distributions of ...
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### KL divergence between gaussian and uniform distribution

Is the KL divergence not defined because uniform has bounded support and gaussian has unbounded support? How else can I calculate the distance of my gaussian to a 'maximum entropy' distribution if I ...
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### Probability of seeing a bird on a certain date based on historical notes

I have a database filled with different bird species that were seen on different dates (10 years of records). Each row in the table contains: Date, Time, Bird Species, Spot where it was seen So it ...
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### Why does discrete data distribution has differential entropy of negative infinity?

Recently I've been reading a paper. In section 3.1, it says "Since the discrete data distribution has differential entropy of negative infinity, this can lead to arbitrary high likelihoods even on ...
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### Why is this probability distribution biased towards even numbers?

I am working on the probabilities of a game where they pick 20 unique number(non-repeating) from range 1 to 80 sort those 20 numbers in ascending order sum every 4 numbers and take the last digit as ...