# Questions tagged [probability]

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

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### How to sample from different datasets such that they have similar distributions?

I have data from multiple datasets with the boxplot given below In the above figure, I have data from 7 different datasets. I am looking for a sampling strategy such that samples from each dataset ...
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### What are the cv.glmnet coefficients?

Let's say one performs a ridge logistic regression with cv.glmnet with standardized variables in R. Here, the outcome of the model is given in coefficients. ...
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### Unsure of how $E_*\{\hat f^*(x;h) - f(x;h)\}^2$ is being explicitly evaluated in a paper on bootstrapping for density estimation

I'm reading a 1989 paper by Charles Taylor 'Bootstrap Choice of the Smoothing Parameter in Kernel Density Estimation' and I'm not sure how he arrived at a certain result. Let $X_1,X_2,\dots,X_n$ be a ...
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### Most likely outcome under Bernoulli trials [closed]

If we have a Bernoulli trial with outcomes $A$ and $B$. Outcome $A$ occurs with probability $p$, and $B$ with probability $1-p$. I read that if $p<0.5$, (so for example, $p=0.499$), then the most ...
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### Can someone Help me out to understand the lecturer says we're talking about Population quantiles, Population median wrt Probability density functions? [closed]

The definition of quantile given here is, Ath Quantile is at a point where the probability ( or area under distribution ) up till that point is A.
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### What features can be extracted from a probability distribution? [closed]

I have been looking online regarding feature extraction and I am looking at extracting features from probability distribution by getting the characteristics of the distribution. I know that most ...
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### Find the Probability density function of a mean random variable

lets say $Y_{1},\ldots,Y_{n}$ are simple random samples with the PDF: $f_{\theta}(y)=\theta y^{\theta - 1} \mathbb{I}(0 \le y \le 1)$ How can I find the PDF of $\bar{Y}$? is it even possible?
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### Gaussian Distribution: How to calculate the Cumulative Distribution Formula (CDF) from the Probability Density Function (PDF)? + Error Function? [duplicate]

I understand that we can calculate the probability density function (PDF) by computing the derivative of the cumulative distribution formula (CDF), since the CDF is the antiderivative of the PDF. I ...
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### The relationship between two probability mass function (poisson distribution)

There are two cylinder bottles with radius r1 and r2 was on the ground to collect rain drop.what is the relationship between the probability mass function of two bottle? I guess that each of the ...
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### Is this notation , $\ell(y,f(x;\theta))= -\log p(y|f(x;\theta))$, correct for the negative log probability loss function of a classifier?

In Murphy’s Probabilistic Machine Learning: An Introduction, he states that the loss function for a probabilistic classifier $f(x;\theta)$ is the following: \ell(y,f(x;\theta))= -\log p(y \mid f(x;\...
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### Bounds of the optimisation problem in NICE paper

In the paper https://arxiv.org/abs/1410.8516, a model called Non-linear independent component estimation is proposed. Following are the governing equations for the forward pass in the network. --------...
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### CLT for non iid random variables

Assume $U_k$ are correlated standard normal random variables. Let $R_k := a_k U_k$. I'm looking for CLT of the sum $S_p := \sum_{k=1}^{p}\frac{R_k}{\sqrt{p}}$. Since $U_k$ are correlated, I'm looking ...
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### Metrics for multiclass classification model accuracy

Usually the last layer in multiclass classification models is a softmax, which is essentially a vector with elements the confidences for each class. The standard top-1 accuracy takes account only if ...
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### Estimators of location and scale versus mean and variance

This question is rather semantic than statistical. In Robust Statistics, estimators of mean and variance of a distribution are often called respectively "estimators of location" and "...
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### joint probability and conditional probability

I came to ask this question because I couldn't understand an answer in What are the differences between "Marginal Probability Distribution" and "Conditional Probability Distribution&...
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### Markov Chain for Amino Acid Sequence

I was wondering if it is possible to apply Markov Chain to this amino acid sequence "ddvlsldeddddsdyncgednd" to find the probability of this sequence forming in this particular positional ...
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### Differences Between the Central Limit Theorem and Consistency

I have recently finished studying the central limit theorem and the idea of consistency. I am still a little fuzzy about them, so I was wondering what are some key similarities and differences of the ...
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### Markov model for patients on a transplant waitlist?

I am developing a Markov model in Treeage based upon survival data for individuals on a transplant waitlist (running first order monte carlo). Over the time horizon, individuals may either become ...
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### Does lack of data affect covariance matrix estimate?

I am building some experiments using the multivariate normal probability density function to estimate the likelihood of a given sample to come from a distribution. For that, the PDF is built using as ...
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### Calculate the sentiment knowing the single probabilities

I am working on finding the sentiment of some text. Right now I am using a python library called VADER that for each sentence it gives me back the probability that a specific phrase is positive, ...