Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [probability-distributions]

Questions on using, finding, or otherwise relating to probability distributions, probability density functions (pdfs), cumulative distribution functions (cdfs), or other related functions. Use this tag along with the tags (probability), (probability-theory) or (statistics).

Any probability distribution, including beta, binomial, chi, Erlang, gamma, geometric, lognormal, negative binomial, normal (Gaussian), Pareto, Poisson, Student's t, uniform, Wald, Weibull, zeta, and Zipf.

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Cases for Division of Continuous Independent Random Variables

I am trying to solve this question that asks for a new variable V such that V = $\frac{Y}{X}$. The given information is $\begin{align*} f(x,y)&=\frac{2x+y}{36} & 0 \leq y \leq x, \hspace{5mm} x + 2y \leq 6 \\ \end{align*}$ . My…
air bmx
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Finding the cumulative distribution function of an exponential with indicator function

I'm given the following probability density function of $x$: $$f(x)=\frac{1}{2}e^{x}\mathbf{1}_{\{x<0\}}+\frac{1}{2}e^{-x}\mathbf{1}_{\{x\geq 0\}}$$ How do I find the cumulative distribution of the following function? I'm confused on how to handle…
Anon
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density of the product of uniformly distributed random variables

Let $X$ and $Y$ be independent with uniform distribution over $(0,a)$ and set $Z=X^2Y^2$. What is the joint density of $Z$ \begin{align} F_{Z}(t) &= \mathbb P(X^2Y^2a^4 \end{cases} \end{align} Consider the case…
Sneach hcaens
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finding the posterior distribution of theta

Let $Y$ be the sum of $n$ independent observations frm a $pois(\theta)$ distribution. Further let the prior distribution for $(\theta)$ be $\gamma(\alpha,\beta)$. I need to find the posterior distribution of $\theta$, given that $Y=y$ AND find a…
user67411
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pareto distribution - problem reformula the density

During my studies we define the Pareto distribution as $F(x) = 1-(1+\frac{x}{\beta})^{-\alpha}$ with density function $ f(x)= 1-(1+\frac{x}{\beta})^{-\alpha} *1_{x>o} $. I don´t understand how we get this density function. If i calculate the…
Mufasa
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Moments of noncentral chi distribution

In the wikipedia article Noncentral chi distribution the raw moments are given by Laguerre polynomials $L_n^{(a)}(z)$ with $n=1/2$ and $n=3/2$ but a Laguerre polynomial is only defined for $n \in \mathbb{N}$. How to understand this or how to…
granular_bastard
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How can we "derivate" the P.M.F. (discret random variable) from the C.D.F?

If we can find the C.D.F. by integrating the P.D.F. (or the other way around by derivating the C.D.F). How can we find the Probability Mass Function of a discret variable from the C.D.F.? I know I'm able to find the C.D.F. from a probability…
Limanido
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What does it mean to take $\| \cdot \|_{L1}$ of Bernoulli r.v.?

What does it mean to take $\| \cdot \|_{L1}$ of Bernoulli r.v.? I saw an example that said that if $\epsilon_k$ is Bernoulli taking values $1$ and $-1$, then $\| \epsilon_k \|_{L1}=1$ for all $k$.
mavavilj
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PDF of V-U for uniform random variables on different ranges

$U$ and $V$ are uniform random variables over $0
Mobeus Zoom
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How can I prove that X and Y are standard normal variables?

If $\theta$ has $U(0,2\pi)$ distribution and $r^2$ has $\operatorname{Exp}(\frac{1}{2})$ distribution, show that $X=r\cos\theta$ and $Y=r\sin\theta$ are independent and identically distributed $N(0,1)$ variables. I know the joint distribution of…
AP _
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Probability distribution between two unit vectors using the taxicab metric for distance

Suppose we have two positive, real unit vectors $X$ and $Y$ in $\mathbb{R}^n$. EDIT: As was suggested in a comment, let me describe how $X$ and $Y$ are randomly generated. For both vectors, pick $n$ random values from the uniform distribution…
QC_QAOA
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Exponential probability density functions of independent variables

I just have a small technical question. I am in the midst of solving a problem where I have gotten 2 different exponential probability density functions that are as follows: pdf #1: 3e^(-3x) pdf #2: 5e^(-5y) The question then asks of me to find the…
nicefella
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Self-Study: "Chi-square distribution is a transformation of Pareto distribution"

I ran across the following statement on Wikipeia at the following location "chi-square distribution is a transformation of Pareto distribution" I have looked for this transformation but cannot seem to find it. I have also looked here but it doesn't…
dsmalenb
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Derivation of the Weibull distribution using the Gaussian distribution as a starting point

I am interested to know how one can derive, from first principles, the Weibull distribution. As I understand it, the Weibull distribution $$D_{w}(x) = \frac{k}{\lambda} \left(\frac{x}{\lambda}\right)^{k-1} e^{{(-x/\lambda)}^{k}}$$ is a generalised…
user27119
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Does there exist a probability distribution could not be associated with a cumulative distribution function?

This wiki page says A continuous probability distribution is a probability distribution with a cumulative distribution function that is absolutely continuous. Equivalently, it is a probability distribution on the real numbers that is absolutely…
JJJohn
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