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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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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 ...
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?
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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 .... ...
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://...
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 $Uniform(0,1)$.
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?
386 views

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 ...
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 $(\overline{x},\overline{y})$. ...
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 ...
199 views

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 ...
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? ...
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 $\rho$? $$Y = \sum_{i=1}^n X_i$$ ...
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 ...
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 ...
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 ...