# Questions tagged [pdf]

Probability density function (PDF) of a continuous random variable gives the relative probability for each of its possible values. Use this tag for discrete probability mass functions (PMFs) too.

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### What does i.i.d. mean for multivariate case?

When we say a random variable is i.i.d., it's often used to describe the dependency between the observations of that random variable, which I call the row dimension, indexed by time if it's a time ...
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### Is The Jacobian Needed to Find CDF for R in Polar Coordinates?

I'm attempting to use inversion sampling to generate points on a disk according to the following PDF: $$f(r) = \dfrac{2}{\pi(1+r^2)}$$ Here, the polar angle would just be a uniform random variable ...
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### Simulating p-value statistics for Liliefors test (Python statsmodels)

Python statsmodels has an implementation of Lilliefors' test for goodness of fit (i.e. if the parameters of the distribution were obtained from fitting the data and not per-determined as in the ...
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### How to Evaluate a Probability Density Function you Fitted?

I was reading "A Student's Guide to Bayesian Statistics" by Ben Lambert and he brought up something I never thought of before and can't find the answer to on Google. That is, evaluating a ...
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### How to estimate parameters and pdf of a random variable transformed from a lognormal random variable?

I have a continuous random variable Y that follows lognormal distribution with known parameters (mu and sigma). Let Y be transformed to X=Y-20000. So it is basically shifted to left. How do I find the ...
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### Finding PMF, CDF of a piecewise function of an RV

Here's the question: Let $Z$ have CDF $F$ and pdf $f$ and let $A$ be a subset of the real line. Further, let \begin{cases} W = 1 & \text{if $Z \in A$} \\ ...
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### finding PDF of Y, given Y|X [closed]

$$Y|X\sim Bin(X,n)$$ $$X\sim U([0,1])$$ How can I find the PDF of Y? I know that: $$\Bbb P(Y=k)=E_X[\Bbb P(Y=k)|X]$$
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### How can we perform the integration for showing this equation?

Im reading this paper momentarily, and there is one equation (9) in section 3.1. that I just can't wrap my head around yet: \begin{align} \mathcal{N}(\textbf{y}_d;\textbf{0},\pmb{\Phi \Phi}^T + \...
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### Calculate the likelihood from the density function with known mean and sd

In this link the likelihood of IQ has been calculated by using dnorm function in R. Here they used "%" sign but based on the range of ...
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### How do you work with a function of a uniform distribution? [closed]

I am struggling with parts b and c. How do you solve them? Could you please give the solution?
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### evaluating an empirical multivariate PDF in python

I have multivariate (bivariate in the simplest case) residuals from a VAR time series regression and I'd like to estimate the joint pdf and then be able to draw from this pdf. If I have bivariate ...