# Questions tagged [density-function]

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

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### How to define a PDF for data with unkown distribution?

I have a dataset containing real values and I want to define the PDF associated. Is there any method to find out the PDF for data with unknown distribution?
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### Help understanding approximation of integral of pdf

Assume that $f$ is the pdf of a continuous random variable $X:\Omega\to\mathbb{R}$. Let $\varepsilon>0$. Then: \begin{equation*} \mathbb{P}\left(X\in\left[x-\frac{\varepsilon}{2},x+\frac{\...
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### density function of $W(2/3)$

$W(t)$ - Wiener process on $(\Omega, F, P)$ and measure $Q$ such that $dQ=e^{W(1)-\frac{1}{2}}dP$. How to find density fuction of $W(2/3)$ with respect do measure $Q$?
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### How to calculate the joint probability: $\Pr \left( \tfrac{g_1}{g_3} \geq \theta_1, \tfrac{g_2}{g_3} \geq \theta_2, g_3 > \theta_3 \right)$?

Question: How to calculate the following? $$\Pr \left( \dfrac{g_1}{g_3} \geq \theta_1, \dfrac{g_2}{g_3} \geq \theta_2, g_3 > \theta_3 \right),$$ where $g_i, i \in \{1, 2, 3\}$ is an exponentially ...
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Let $X$ and $Y$ be random variables with marginal pdfs $f_X(x)$ and $f_Y(y)$, respectively, and joint pdf $f_{X,Y}(x,y)$. Then for all $y$ such that $f_Y(y) \neq 0$ define the function $$f_{X|Y=y}(x) =... 1answer 101 views ### Given a multi-dimensional sample, how do I build a distribution density coefficient? [closed] Given a sample X=\{\vec{x}_1, \dots,\vec{x}_l\} where \vec{x}_i \in \mathbb{R}^d with d>3, I would like to know if it's possible to have and index that is inversely proportional to the ... 2answers 35 views ### How to derive the probability density function (PDF) of a continuous random variable from a set of data? I am interested to derive an expression for the probability density function (PDF) of a continuous random variable from a given set of data. To further explain, let us consider that we have the data ... 2answers 60 views ### Probability density of analytical function on 3 random variables I know some methods to obtain the probability distribution of functions on a random variable: CDF method: If X is a random variable and Y=f(X), then computing the cumulative distribution ... 1answer 21 views ### General condition for PDF of a random variable, so that it is self-inverse I am supposed to find a general condition for a PDF of a random variable X, so that the distributions of X and 1/X are the same. I showed this for standard Cauchy distribution using the formula  g(y)... 1answer 32 views ### How do I handle this probability density function with a Jacobian? "Suppose X and Y are independent random variables, each exponentially distributed with parameter \lambda. Determine the probability density function for Z=\frac{X}{Y}." Here is what I have so far:... 1answer 78 views ### Finding pdfs of \frac1{X^2} and \frac{1}{4}\left(\frac1{X^2}+\frac1{W^2}\right) where X,W are independent N(0,1) X,W are independent random variables, both N(0,1), i.e. f_X(x)=f_W(x)= \frac{1}{{\sqrt{2\pi}}}e^{-\frac{x^2}{2}}. Find PDF of Y:=\frac{1}{X^2} Find PDF of \frac{1}{4}\left(\frac{1}{X^2}+\... 0answers 51 views ### How to inverse the laplace transform \frac{1}{\cosh(5\sqrt{s})}? Let X be a random variable with  E[e^{-sX}]= \frac{1}{\cosh(5\sqrt{s})}  and density function f. How to give a formula for f? 1answer 56 views ### PDF of Y=X(X-1) when X has a piecewise PDF I have to solve the following problem: Let X be a continuous random variable with PDF$$f(x)= \begin{cases} x+1, &-1\leq x<0\\ 1-x, &0\leq x\leq1\\ 0, &\text{otherwise} \end{cases}....
I've only ever seen domains stretching from $X\ge0$. I have a question where: $F(x)=cx^2$, Domain: $− 1 ≤ x ≤ 1$ When finding value of $c$, would I only need to integrate $0$ to $1$. And does that ...