Episode #125 of the Stack Overflow podcast is here. We talk Tilde Club and mechanical keyboards. Listen now

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.

Filter by
Sorted by
Tagged with
-1
votes
1answer
78 views

The pdf of a standard uniform random variable divided by constant [closed]

For a random variable $\frac{U}{a}$ where $U$ is a standard uniform random variable, I'm trying to determine the pdf. I'm not so sure what I'm getting is correct as I'm getting some funny results ...
2
votes
1answer
47 views

Is there a name for the distribution whose PDF is -ln(x) on its support [0, 1)?

If so, what is its name? If not, how/where can information about it be found?
0
votes
0answers
9 views

How this Equation is solved? How dBi is changed into rdr?

$Y_i = \frac{|h_{B_i}|^2}{1+d_{B_i}^\alpha}$ $d=distance, h_Bi=gain$ $f_{W_{B_i}}(\omega_{B_i}) = \frac{\lambda_{\Phi_B}}{\mu_{R_{D_B}}}=\frac{1}{\pi R_{D_B}^2} $ \begin{align} (CDF) of Y_i .... ...
1
vote
0answers
48 views

Exponential Family Representation: Dumb question on scale parameter and whether it went to Hawaii

So going over the Hastie Tibshirani paper on GAM - it points to equation 11 as the exponential family density - but with two parameters - theta (natural parameter) and phi (scale). https://...
1
vote
1answer
55 views

Transform X to get Y such that Y has a Uniform(0,1) distribution

A random variable $X$ has the PDF $f_X(x) = \frac{x - 1}{2}, \ 1 < x < 3$ Find a monotone function $u(x)$ such that the variable $Y = u(X)$ has the distribution $Uniform(0,1)$.
1
vote
1answer
44 views

Measure of dispersion around the mode

I usually associate the standard deviation with the mean and the IQR with the median. Is there a measure of dispersion typically associated with the mode?
2
votes
1answer
386 views

CDF and PDF of radius of a unit disk

Let X and Y be uniformly distributed on a unit disk such that $x^2 + y^2 \leq 1$ Let $R = \sqrt{X^2 + Y^2}$. What are the CDF and PDF of $R$? I know that the area of the unit disk is $A = \pi r^...
2
votes
0answers
585 views

Point process - intensity function vs probability density function

Suppose we have a point process in $\mathbb{R}$ with intensity $\lambda(x)$. Then, for a given compact set ${ S}$ we have $$\Lambda({ S})=\int_{\rm S} \lambda(x) \, dx,$$ where $\Lambda({ S})$ is ...
0
votes
1answer
22 views

How to make recognition of the important document's attributes

We have a set of PDFs with the different types of documents from the various companies. The goal: to predict which of them contain some important attributes (for example, document number, customer ...
6
votes
0answers
129 views

Finding MLE and MSE of $\theta$ where $f_X(x\mid\theta)=\theta x^{−2} I_{x\geq\theta}(x)$

Consider i.i.d random variables $X_1$, $X_2$, . . . , $X_n$ having pdf $$f_X(x\mid\theta) = \begin{cases} \theta x^{−2} & x\geq\theta \\ 0 & x\lt\theta \end{cases}$$ where $\theta \...
1
vote
1answer
584 views

Histogram and probability mass function

I have a dataset of a discrete random variable. My question is: Is the normed histogram(I divide the frequencies by the total number of samples) and the PMF is the same quantity? It seems they are. Is ...
0
votes
1answer
79 views

Visualize Covariance when only probability mass and marginal functions are given

I am trying to intuitively understand Covariance like here. So if a random sample set given, I could draw rectangles with them, one of the cornes being fixated on mean $(\overline{x},\overline{y})$. ...
1
vote
0answers
15 views

Why does the Y axis change in population density plot when changing from raw scores to z-scores (assuming normal distribution) [duplicate]

Why do values on the Y-axis change in a probability density plot when changing from raw values to z-scores? The mean z-score aligns with 0.40 on the Y-axis, while the Y-value for the mean with ...
4
votes
1answer
199 views

Conditional Expectation of pdf

Wish to identify what I'm doing wrong when finding the $\operatorname E(X\mid Y=5)$ of the following: $$f(x, y)=\begin{cases} 1/6 & \text{if } 0<x<2, 0<y<6-3x \\ 0 & \text{...
1
vote
0answers
42 views

Order statistics for log series distribution?

I am trying to obtain the probability mass function for various order statistics of a log series distribution for a given $n$. To do so, I tried modifying the code given in this question: Simulating ...
4
votes
1answer
643 views

Median of Rayleigh Distribution

I am not sure how to solve the following problem: The probability density function of the Rayleigh distribution is, $\ f(x;α) = \frac{x}{α^2} e^\frac{-x^2}{2α^2}, x ≥ 0, $ where α is the scale ...
1
vote
0answers
10 views

Is there an informative term for calling the random elements conditional on which a PDF of a random element is defined?

Let $X_{1}, \dots, X_{n}$ be i.i.d. random elements; suppose the conditional PDF $f_{X_{1} \mid X_{2} , \dots, X_{n}}$ exists. Then I wonder if there is already in literature an informative name for $...
0
votes
1answer
39 views

Compute Mean of Normal Distribution where x% of Values are over y

I am looking for a way to determine the mean of a normal distribution (with given variance), where e.g. $z = 0,37 = 37\% $ of values should be above a certain value $a$ (e.g. 0,2)? My first idea was ...
1
vote
1answer
168 views

Is there a skewed probability density function that models a normal distribution with two parameters, $σ_1$ and $σ_2$?

Is there a way to model data that are skew normally distributed, but for which one builds in two seperate standard deviations? The parameter $σ_1$ should specify the 15.9% to 50% interval, whereas $...
2
votes
2answers
74 views

Variance being negative

Let $X$ and $Y$ have joint pdf such that $$f(x,y) = 3e^{-3x-y}, 0 < x< \infty, 0< y< \infty.$$ (a) Show that $X$ and $Y$ are independent. (b) Calculuate $Var(X)$. In ...
0
votes
1answer
136 views

What does PDF of normal distribution represents? [duplicate]

I have a basic question about the probability density function of the standard normal distribution $X\sim N(0,1)$. I understand that the cumulative distribution function for x is $P(X\le x)$ (in R ...
4
votes
1answer
98 views

Is the parameter vector of an indentifiable distribution of a transformed random vector always a subvector…?

I would like, after further considerations about this problem, to reformulate this question of mine again. I kept a record of the past words and remarks as the appendix below. I think the question ...
0
votes
1answer
77 views

Probability of first time to an event

We have a stream of events over time. Suppose that $f_t$ is the probability density that an event happens at time $t$. For example, $f_t$ can be the probability density that any bus arrives at time $t$...
0
votes
1answer
41 views

Applying assumptions about marginal and conditional PDFs

We are given $0 < x_2 < x_1 < 1$. What assumptions can you make about $f_1(x_1)$ and $f_{2|1}(x_2|x_1)$? I know that $f(x_1) f_{2|1}(x_2|x_1) = \frac{1}{x_1}$. I know the expression can be ...
1
vote
0answers
15 views

Is it possible to find the joint distribution of a random vector if only the distribution of scalar many-to-one transformation is known? [duplicate]

Theoretical Exercise: I'd like to derive the joint distribution $p_{\boldsymbol{X}}$ of a random vector $\boldsymbol{X} \in \mathbb{R}^K$ if only the distribution of a scalar many-to-one ...
1
vote
1answer
33 views

How to scale between a equal distribution and an empirical distribution

I am not that good at expressing things mathematically, so I'll start with the practical problem right away: I have a set of four objects: O1, O2, O3, O4. Now I want to assign a variable that scales ...
22
votes
1answer
4k views

How many times must I roll a die to confidently assess its fairness?

(Apologies in advance for use of lay language rather than statistical language.) If I want to measure the odds of rolling each side of a specific physical six-sided die to within about +/- 2% with a ...
0
votes
3answers
112 views

what does p( y | μ,σ²) really mean?

Just started to study Bayesian Statistics. I am very confused the concept of having a conditional probability on a distribution. Specifically: I understand what p( A | B ) where A="I am sick" and ...
1
vote
1answer
273 views

multivariate normal distribution range [duplicate]

Simple question about MVN pdf. I understand the domain to be [0,1]. However, why does scipy.stats.multivariate_normal.pdf output values above this range. E.g. <...
5
votes
1answer
77 views

Distribution of maximum frequency of uniformly distributed integers

If I roll an M sided dice N times, there will be at least one number that occurs most frequently. What's the distribution of that maximum frequency in terms of M and N? (its pmf and name if it has one)...
2
votes
0answers
118 views

Finding probability of a point using bivariate copula density

I have a data in the form $\textbf{N} \times 2$. I am using bivariate copula to model the joint density of this distribution. Firstly, I fit 2 marginal distributions independently on each column of ...
1
vote
0answers
29 views

What is “data distribution”? Does it Belong to Probability Space?

While reading the paper BEGAN : Boundary Equilibrium Generative Adversarial Network the autor writes as following: "the generator $G(z)$, which maps a sample $z$ from uniform distirubiton to the data ...
1
vote
0answers
119 views

Computational complexity of sampling from discrete and continuous distributions?

What is the computational complexity of sampling from any of these cases? I mean the computational complexity of the most efficient existing algorithm, not a possible algorithm or a lower bound. ...
1
vote
0answers
24 views

Drawing density plot in R [duplicate]

I drew a histogram of my data: ...
0
votes
1answer
54 views

Generate PDF from CTMC

I have an irreducible continuous-time Markov chain (CTMC) with a finite state space. The CTMC also does not have any one-step transitions from any state to itself. I have the transition rate matrix $Q$...
3
votes
1answer
161 views

how to get joint pdf of mixed random variables

I would like to know how the joint probability density function $p(b,r,\sigma^2)$ can be calculated for the following graph. Random variable $b$ is a latent binary variable, and random variable $\...
0
votes
1answer
714 views

Statsmodels' Negative Binomial: after .fit_regularized(), how to turn PMF into PPF to get the discrete values?

I used the package statsmodels to fit a Negative Binomial to my data. This data contains ~1500 samples with 21 covariates. Since I have overdispersion in my data ...
0
votes
1answer
195 views

pmf for coin toss

I am currently studying Statistical Inference class on Coursera. In one of the assignments, the following question comes up. Let $x=0$ represent a 'heads' outcome and $x=1$ represent a 'tails' ...
1
vote
1answer
27 views

How can I find this constant?

My friend asked this question in our class: let X be a random variable which has a cumulative distribution function . Find (a). I think (a) cannot be solved but my other friend thinks (a) = 5/8 ...
3
votes
1answer
932 views

How to estimate probability density function (pdf) from empirical cumulative distribution function (ecdf)?

The context is survival analysis, where I have an empirical survival function in the form of a step function, which is just one minus the ecdf. Is there a standard way to get an estimate of the pdf (...
0
votes
1answer
524 views

Deriving Posterior Binomial Density from Uniform Prior

I'm trying to derive the posterior density of the probability parameter of a binomial random variable, given one realization of the random variable and a uniform prior density on the probability ...
1
vote
2answers
61 views

Finding pdf with more than one random variable

I am stuck with a question doing one of my stats tutorial and question is as follows: Suppose X and Y are two independent exponential random variables with parameter $\theta$, i.e. their joint ...
4
votes
1answer
47 views

A symmetric iid process

Let $X_1, X_2, \ldots$ be an iid process with $X_i$ having a symmetric distribution around $0$. Then can I always write $$X_1 - \alpha X_{t-1}-\alpha^2 X_{t-2}-\cdots \stackrel{iid}{=} X_1 + |\alpha| ...
0
votes
1answer
282 views

Difference between probability density functions and sampling distributions

I was wondering what is/are the fundamental difference(s) between a probability density function for a mean and sampling distribution of a mean? Can we say that ...
2
votes
1answer
93 views

How do you check that a sampler and a density correspond to the same random variate?

General Question If someone handed you a direct sampling algorithm and a density function, and they told you that the two corresponded to the same random variate, how would you check this? ...
5
votes
1answer
453 views

What is the distribution of a sum of identically distributed Bernoulli random varibles if each pair has the same correlation?

What is the distribution of a sum of $n$ Bernoulli random variables, each having success probability $p$, where each pair is correlated with correlation coefficient $\rho$? $$Y = \sum_{i=1}^n X_i$$ $$...
0
votes
1answer
35 views

Why does the PDF use a different variable than x?

In the below image (from Wikipedia but also found in my text book), I noticed that the variable within the integrand is a "u" rather than the "x" which is found in the CDF function. Why is the ...
1
vote
0answers
66 views

What is the expected fraction of observations in the top x% that remains in the top x% after a random shock?

I'm struggling with a probability question, and I was hoping someone here could help me out. Here's the setting. Suppose you draw observations from a probability distribution Z and sort these ...
1
vote
1answer
105 views

If $X=Y+Z$ with known pdf of $X$, are $Y$ and $Z$ unique?

Say there are random variables such that $X=Y+Z$ with $Y$, $Z$ independent; knowing the pdfs of $Y$ and $Z$, one can (technically) find the pdf of $X$. Taking it from the other side: if one knows the ...
3
votes
1answer
167 views

When we take draws from a normal distribution what are we drawing? [closed]

As I dig deeper than surface level in probability I'm starting to ask more questions I never thought about before. There are a bunch of intertwined concepts that are quickly becoming confused in my ...