# Questions tagged [density-function]

For questions on using, finding, or otherwise relating to probability density functions (PDFs)

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### Applications: Cauchy-Schwarz inequality and Triangle inequality

I am reading a proof from "Transporting Probability Measures" (PhD's thesis of Gilles Mordant) with the following steps that I am not sure to understand. Let $X \sim P$ where $P$ is a ...
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### Computing conditional PDF of continuous R.V.s

The problem is explained as such: A soccer player is shooting at a round target. The player chooses the radius of the target, notated $R$ from an exponential distribution $R$ ~$Exp(2\lambda )$. ...
• 369
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### How to deduce the joint distribution of two different elliptically contoured distribution. See details in following.

if $X \sim EC(0,\Sigma_1, g_1)$ and $Y\sim EC(0,\Sigma_2,g_2)$, then what is their joint distribution？That is, let $Z=(X,Y)^T$, what might the distribution of $Z$ be? Clearly, when $X$ and $Y$ are ...
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### Conditional PDF notation when conditioning on variable falling within certain range

I understand that the conditional PDF of some RV $X$, given some variable $Y$, is written as $f_{X|Y}(x|y)$. Also, I understand that if I want to describe general features of that function, I am to ...
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### Finding the PDF of a sum of 2 different distributions

Let $X,Y$ be two continuous independent R.Vs such that $X$~ $Uni(-1,3)$ and $Y$ is a R.V. defined within $[0,1]$ with PDF: $f_Y(y)=\frac {1}{\sqrt {y}}$, Find the PDF of $Z=X+Y$ In my first attempt, ...
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### Probability: Finding the probability density function when we have the expectation

I'm attempting to solve this problem, and I'm not sure how to (sort of) backtrack the PDF when I have the expectation. Let $Y$ be a continuous R.V. given by the PDF: $f_Y(y)=2(1-y)$ where $y\in [0,1]$ ...
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### Power law dependence in the distribution of $x = GPF(n) / \sqrt{n}$, where $GPF(n)$ is the greatest prime factor function
Consider the set of integers between $2$ and some large number $N$. For each such number $n$, we can compute the quantity $x = GPF(n)/\sqrt{n}$, where $GPF(n)$ is the greatest prime factor function. \$...