# Tagged Questions

PDF stands for Probability Density Function (as compared to CDF for Cumulative Distribution Function). The PDF of a variable gives the likelihood for each value of a continuous variable. Use this tag also for PMF (Probability Mass Function) the analog for discrete variables.

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

On the Wikipedia page about naive bayes classifiers here there is this line "P(height|male) = 1.5789 (A probability distribution over 1 is OK. It is the area under the bell curve that is equal to 1.)" ...
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### Deriving Negentropy. Getting stuck

So, this question is somewhat involved but I have painstakingly tried to make it as straight-forward as possible. Goal: Long story short, there is a derivation of negentropy that does not involve ...
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### Estimating PDF of continuous distribution from (few) data points

What are some good, established methods for estimating the probability density function (denoted $f(x)$ from here on) of a continuous distribution, given a sample of points $x_1, \ldots, x_n$ drawn ...
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### Show that, for $t>1$, $P[\frac{Y}{Z}\leq t]=\frac{t-1}{t+1}$

Let the distribution of $X$ be $U(0,1)$. Let U be the length of the shorter of the intervals $(0,X)$ and $(X,1)$; that is, $Z=min(X,1-X)$ and let $Y=1-Z$ be the length of the larger part. Show that, ...
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### Сonfidence interval of histogram probability density function estimator

There is a circle of radius $R$ and a sequence of points within it. I'm going to estimate a PDF of appearing at elementary area at the distance $D$ from the centre of the circle using a realization of ...
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### Problem calculating joint and marginal distribution of two uniform distributions

Suppose we have random variable $X_1$ distributed as $U[0,1]$ and $X_2$ distributed as $U[0,X_1]$, where $U[a,b]$ means uniform distribution in interval $[a,b]$. I was able to compute joint pdf of ...
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### PDFs and probability in naive Bayes classification

I have seen a few times the technique of using the Gaussian PDF for continuous features in Naive Bayes. here and here. Illustrated in the first link: How is this possible? I always learnt that the ...
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### Calculating event probabilities in mixed, discrete/continuous distributions

This is a simple question. I am dealing with a "clipped" normal distribution -- say, $N(0,0.5)$ clipped between $[-1,1]$. I would like to calculate the "probability" of a sample, but I know that in ...