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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.

28080 questions
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Probability distribution of a specific die roll

A person rolls a die until he gets a result he has gotten before. Let $X$ be the amount of rolls and find the probability distribution of $X$. I was first thinking this was a geometric distribution, but I am not sure how I am supposed to construct…
DerpyMcDerp
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binomial distribution transformation

Let X and Y be independent random variables with X having a binomial distribution with parameters 5 and 1/2 and Y having a binomial distribution with parameters 7 and 1/2. Find the probability that |X − Y | is even.
kris91
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Stable random variable with bounded values

Recently I've came across "Stable distributions" and have seen ways of generating them. I am interested in the so-called "p-stable" distributions (e.g. see here), i.e. those such that if $x_1$ and $x_2$ are copies of a random variable $\zeta,$ then…
Ilonpilaaja
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POints in a circle connected as per a certain condition

Suppose we chose $n$ points uniformly and randomly in a unit circle $\mathbf{S}$ centered at the origin $(0,0)$ and chose a number $r$,$0\leq r\leq1$.Connect two points by a line segment iff the product of their radial distances is less than $r$.…
AgnostMystic
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Find PDF of $Y = X_1-X_2$

$X_1$ and $X_2$ are i.i.d random variables and the pdf of each of them is $e^{-x}$ for $x>0$ and $0$ otherwise. $Y = X_1-X_2$ and the question asks to find the pdf for $Y$? I took the approach of going from the cdf to pdf. $P(Y\le y) = P(X1-X2\le y)…
actB4157
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Infer the joint distribution of random vector from the sum of its co-ordinates

Let $a, b, c \in \mathrm R$ be such, that $a^2+b^2+c^2=1$. Let $U=(X,Y,Z)$ be a random vector, about what we know is only that $aX+bY+cZ$ is uniformly distributed on $(-1, 1)$ line (for each a,b,c satisfying the condition $a^2+b^2+c^2=1$). Show $U$…
Jakub Wierzbicki
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Distribution of product of Rician(Rice) Random Variable

Let $X \sim Rician(\mu,1)$. I want to ask about the distribution of product of $X$ as $Y = aX$. $Z = b - aX$. From my intuition, $Y$ might also be the Rician distribution with parameter as $(a \mu, a^{2})$. However, I am not really sure about this…
M.bara
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Joint probability Statistics

There are a total of 12 quotes, half of which were said by President Trump and half by Gordon Gekko. let X denote a random variable which indicates the number of right answers one has on quotes from President Trump. Let Y denote a random variable…
mustafa badakhsh
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if we flip the coin $100$ times, what is$ P(X\leq 10)$?

we have a coin of diameter $d$ and a table of infinite grid of identical squares, each square has side $s$. suppose that $2d = s$. let $X$ denote the total number of times that the coin ends up within a square. if we flip the coin $100$ times, what…
Sean Jones
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functions of several random variables

Let $R$ and $X$ be independent non-negative random variables such that $R^2\sim \chi^2_2$ and $X\sim U(0, 2\pi)$. Fix $a$ belonging to $(0, 2\pi)$. Find the distribution of $R\sin(X+a)$.
kris91
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CDF of a Uniform Distribution Dependent on Another for its Upper Bound

I would like to know how to calculate the CDF $F_y(y)$ of the following (if possible): $$Y \sim U[1.4,\ x], \text{ where } X \sim U[1.4,\ 2].$$ I have tried to calculate $f_Y(y)$, taking the following steps: $f_X(x) = \left \{ \begin{array}{l} …
Bill Smith
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Weibull distribution probabilities

I am reading the following paper on page 15 it is written that for Weibull distribution with scale and shape parameters estimated at 13.6 and 2.6, they estimate the following…
Wiliam
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marginal distribution of $X$ . given probability density function

The continuous random variables $X,Y$ have joint probability density function $f(x,y)=e^{-2x^2-2y^2}$. Then what is the marginal distribution of $X$ What i try: Marginal distribution of $X$ is given by…
jacky
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Right-skewd or power law distribution

Is a power law distribution right skewed? Is there any relation between concepts of right skewness and power law distribution?
user25004
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Need help understanding the solution to a probability question.

$(x)$ is for number of complaints in a month. $P(X=x)$ is the probability So $0.16$ probability for $0$ complaints a month. $0.24$ probability for $1$ complaint a month and so on. The question is: What is the probability that the insurance company…
mangekyou
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