# Questions tagged [density-function]

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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### Coin flipping example (Bernoulli distribution) [closed]

I have a problem with two coins. One of them is an ordinary coin, while the other coin favors the heads side by a factor of 2/3. "U" is the total of observed outcomes and "V" is a ...
18 views

### Probability of a vector. Is my notation correct?

Question 1: Let us first consider the univariate case: Suppose we have $Y\in\{0,1\}$, suggesting that $Y$ is Bernoulli variable (and hence discrete) and $X\in \mathbb{R}$, then we know that \begin{...
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### Alternative formula for the Bernoulli pmf?

If I understand correctly, a Bernoulli pmf just needs to assign a probability $p$ if there is a success $(x=1)$, and $1-p$ otherwise $(x = 0)$. Rather than the usual formula, can't the following ...
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1 vote
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### Deriving distribution under change of variables between spaces of unequal dimension

For a function of random variables $T:\mathbb{R}^n \mapsto \mathbb{R}^m$ Wikipedia outlines how to handle three cases: $m = n = 1$ $m=n > 1$ $n>1 \land m=1$ There seems to be two missing cases:...
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### What is the probability density function of a parallelogram [closed]

A very short question: What would be the probability density function of a parallelogram? Could we consider it as a two triangular distribution (in pink) that behaves the same and a uniform ...
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1 vote
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### How to interpret height in probability density function? [duplicate]

Assume I have a continuous variable X with PDF f(x). I know that, for every value of x, P(X=x) = 0, so the value f(x) is not the probability. But what is it exactly? If we have f(a) = 2 * f(b), can we ...
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### PDF of $Z=X^2 + Y^2$ where $X,Y\sim N(0,\sigma)$

Using normal distribution probablilty density function(pdf), \begin{align} f_Y(x) = f_X(X) &= \frac{1}{\sigma\sqrt{2\pi}}e^{-\frac{x^2}{2\sigma^2}} \\ \end{align} Taking $Z' = X^2 = Y^2$, the ...
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### Derive the pdf/cdf of a variable given as a formula of two random variables [closed]

Let's assume I have two random variables X and Y with x>0 and y>0, respectively. Let's also assume that their marginals are known as well as the joint cdf is known as the product of the two ...
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### Fast measure of "clusteredness" of points?

I have a cloud of points in a bounded volume in 2D (lets say 2d for now, though it'd be nice to generalize to any dimension): $<p_n \in \mathbb [0, 1]^2: n \in [1..N]>$ I'm looking for some ...
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### Complete workflow for best distribution fits

I'm studying streamflow data and i want to: (1) find best distribution for Annual (and montlhy) Q7 (minimum mean of 7 days flow per year) series; (2) obtain Goodness-of-fit for the best distribution ...
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### Evaluating/combining PDFs over time to predict future value

I am trying to predict a value over time. I have historical data that I have used to calculate PDFs for the change over various time intervals. If I'm trying to predict the value at time T0 and start ...
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### I need help understanding why this integral is the probability for winning by switching in the Monty Hall problem

I need help understanding this probability from the Monty Hall problem. Why does this integral give the probability of winning by switching if the Car is behind 1, Monty shows goat behind 3 and Player ...
1 vote
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### How can I derive the distribution of the L2,1 norm if the ditribution of L1 norm is given?

I understand that the L1 norm promotes sparsity and is a Laplace prior in the LASSO regression framework. I am interested in how this prior changes when we apply L2,1 regularisation instead? Is it ...
1 vote
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