# 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.

1,139 questions
Filter by
Sorted by
Tagged with
30 views

### Why density plot tails are beyond maximum and minimum values?

I am trying to interpret the tails of a density curve, which go beyond xlims(0 in this case). I understand that area under the curve between any two points represents the probability of that event. ...
124 views

### Combine Multiple Discrete Probability Density Functions

I'm a bit stuck trying to figure out the combined probability from several discrete PDF's. Lets say I have a bunch of different classes (Truck, Sports Car, Station Wagon, etc) and a bunch of ...
2k views

### Practical applications of the Laplace and Cauchy distributions

I want to know if there are any examples of real-life applications of the Laplace and Cauchy density functions. How do they differ in their applications? This related post, however, does not answer ...
25 views

### Finding a distribution of a transformation of a random variable [on hold]

Suppose X ∼ Exponential(λ). Find the distribution of the random variable Y = λX, where λ > 0 So do I just multiply the exponential distribution by another lambda?
35 views

48 views

### How can I calculate this PDF

I'm trying to reproduce the results of a ray tracing paper which uses reinforcement learning. I asked my question in the computer graphics community of this site, but I think my problem can easily be ...
176 views

### Estimating an underlying pdf from binomial trials

I'm afraid I'm not an expert in statistics, but I have a particular problem I'm interested in solving. I'm pretty sure this area already has a lot of literature, but I'm having difficulty finding ...
127 views

### Excepted conditional density and conditional expectation

Apparently one can obtain a regression analysis as $$g(x)=\frac{\int yf(y,x)dy}{f(x)}$$ where $$f(x)=\int f(y,x)dy$$ is the marginal density of $X_i$. In effect, I believe, the above expression ...
35k views

### How to find the mode of a probability density function?

Inspired by my other question, I would like to ask how does one find the mode of a probability density function (PDF) of a function $f(x)$? Is there any "cook-book" procedure for this? Apparently, ...
36 views

19k views

### “The total area underneath a probability density function is 1” - relative to what?

Conceptually I grasp the meaning of the phrase "the total area underneath a PDF is 1". It should mean that the chances of the outcome being in the total interval of possibilities is 100%. But I ...
16 views

### Dynamically updating posterior density in R

I want to redefine my function in a loop by calling the function from last iteration. However I know this is basically a recursive way which I don't want. To give an example, see the following ...
34 views

### Find $\alpha$ and $\beta$ so that $f_X(x)$ can be a density function

\begin{equation*} f_X(x) = \begin{cases} \frac{4x^2}{5} & \text{ , if } 0 < x \leq 1\\ \alpha(5-2x) & \text{ , if } 1 \leq x < 2\\ \beta x^2 & \text{...
57 views

### Density estimation as an optimization problem

Density estimation is the estimation of a probability density function from observed data. Can some of the common approaches to density estimation, such as kernel density estimation, be formulated as ...
12 views

### Calculating a baseline probability model for images

I'm a newbie to statistics, so I apologize if this question is trivial. I'm trying to build a distribution that can predict a specific set of images. But first, I need a baseline - so, I decided to ...
23 views

### Bivariate Dist Study Question Help - determine joint PMF and P( … )

I am in a prob. models class. Current module is on Bivariate and Multivariate Distributions. The question below has me stumped though. It is from a study guide and I would like to know the answer ...
47 views

### how to scale the density plot for my histogram

I have the histogram plot and I'd like to overlap it with density line for the same data. Importantly, I don't want to turn histogram into density values, but want to keep N (numbers) on y axis. Is ...
60 views

### What is the name of this distribution?

I came across this: a categorical distribution with $K=10,000$ parameters (categories), and we take only few samples from this distribution, say $N=400$ (the point is $N < K$). Now, obviously, not ...
48 views

### Simulating from an Epanechnikov kernel density estimate in MATLAB / exact form of the Epanechnikov kernel in MATLAB?

It's my first time posting, so apologies if I'm breaking any etiquette. I've used MATLAB's ksdensity function to estimate a density using the Epanechnikov kernel and would now like to make repeated ...
166 views

### Mean and variance of maximum of normal random variables

I'm trying to find the mean and variance of $Y = \max(X_1, ..., X_n)$ where $X_i \sim \mathcal{N}(\mu_i, \sigma^2)$. Note that the $X_i$ are independent, but not identically distributed. That is, ...
856 views

### Whence the beta distribution?

As I'm sure everyone here knows already, the PDF of the Beta distribution $X \sim B(a,b)$ is given by $f(x) = \frac{1}{B(a,b)}x^{a-1}(1-x)^{b-1}$ I've been hunting all over the place for an ...
20 views

### What is the distribution of a point to a random line?

Let's say that we have a random vector that represents a line [A,B,C] so that, Ax + By + c = 0. A, B, and C are independent Normally distributed random variables, with different mean and variances. if ...
1k views

### Marginal distribution of the diagonal of an inverse Wishart distributed matrix

Suppose $X\sim \operatorname{InvWishart}(\nu, \Sigma_0)$. I'm interested in the marginal distribution of the diagonal elements $\operatorname{diag}(X) = (x_{11}, \dots, x_{pp})$. There are a few ...
### How do we find the constants of pdf using the $\mathrm{E}(X)$? [closed]
I have a pdf of cont random variable as $(a+bx^2)$ between $0$ and $1$. how do I find the constants $a$ and $b$ when my $\mathrm{E}(X)=3/5$?
In logistic regression, we set the probability of predicting a target $y$ given a data $x$ as, $\Pr(Y = 1|X;w) = \dfrac{\exp(w^TX)}{(1+\exp(w^TX))}$ What is exactly this probability distribution (or ...