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.

28080 questions
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Is this variable discrete?

I wonder if you can help me with this. I've got homework where I need to determine the type of probability distribution that I should use to model the variable 'time'. The variable however is measured as days in 0.5 day intervals. Would this be a…
Ren1231
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Beta distribution for modelling sequence of probability estimations.

I have a continuously growing list of probability estimations of an event $$[p(e,t1),p(!e,t2),\ldots,p(e,tn)]$$, where $p(e,t)$ is the probability of the event $e$ or not $e$ happening at time t. I't like to have a random variable that models these…
mvc
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convolution for uniform distribution with variable borders

I need to calcuate a convolution of two uniform distributed random variables, both are defined as $f_z\left(z\right)=\frac{1}{h},z\in\left(0,h\right)$, to get the pdf for Z. As a convolution of two continious random variables is defined…
RaNdOmE NaMe
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Is there a probability distribution on a bounded interval, for which the hazard is monotonically increasing but does not diverge to infinity?

I'm really struggling to answer myself the following question! Is there an absolutely continuous probability distribution that is supported on a bounded interval [a,b], for which the hazard function $\frac{f(x)}{1-F(x)}$ is monotonically increasing…
Projectsral
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Urn Problem balls distribution

Consider an urn with two type of balls white and black with proportionality $p,q$ respectively such that $p+q=1$ we extract balls $n$-time successively with replacement. calculate the probability that the k-th extracted white ball appears on the…
HellBoy
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Transforming existing von Mises samples with new $\mu$ and $\kappa$

I am trying to transform samples $x_1$ that have already been sampled from a von Mises distribution $\mathcal{V}_1(\mu_1,\kappa_1)$ to match a another von Mises distribution $\mathcal{V}_2(\mu_2, \kappa_2)$. With normal distributions…
Kiord
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$(X,Y)$ has the following joint p.d.f $f_{X,Y} (x,y)= \dots $ , show that $ f_{X-Y} (u)= \dots $

Q: $(X,Y)$ has the following joint p.d.f $$f_{X,Y} (x,y)= \begin{cases} \frac{2}{(1+x+y)^3}, \ &x,y > 0 \\ 0, \ &\text{elsewhere.} \end{cases}$$ Show that $$ f_{X-Y} (u)= \frac{1}{2(1+|u|)^2}, \ -\infty < v < \infty. $$ Attempted solution: Using…
Oskar
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Rate of change of the failure rate of a gamma random variable

Let T be a gamma random variable with parameters $s>0$ and $\lambda>0$. The PDF of T is $f(t) = \frac{\lambda^st^{s-1}}{e^{\lambda t}\Gamma(s)}$. I need to show that the failure rate of T, $\lambda(t)=\frac{f(t)}{1-F(t)}$ is increasing when…
Heng Wei
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THE PROBABLE ERROR OF A MEAN- seminal 1908 paper from Gosset (Student). Please help me to understand the first identity in Section 1

I am reading the original 1908 paper "The probable error of a mean" from William Sealy Gosset (Student pseudonym) where the Student T Distribution was first derived. On section 1 (at the end of page 2 in the original paper) the author starts with…
Andrea Andrea
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What is the expected value of exp(-x^2) when x is normally distributed?

If $X$ is a random variable following a multivariate normal distribution with parameters $\mu$ and $\Sigma$, what is the expected value of $e^{-X^2}$, that is, what is $\int e^{-x^2} p(x) dx$?
Jabby
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Distribution of the square of a circular random variable

Let $X$ be the random variable corresponding to the radial distance of a point chosen randomly and uniformly in the unit disc.Then the pdf of $X$ is given by: $$ f(x)= 2x, \leq x \leq 1$$ How can we find the dsitribution of $Y=X^2?$ I willbe…
AgnostMystic
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What could be said about the distribution of two iid random variables $X$ and $Y$, given the distribution of $X-Y$?

In particular, if the distribution of $X-Y$ is known, can the distribution of $X$ and $Y$ be determined up to some simple transformations e.g. translation and reflection?
StormRaiser
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Combined probability-flipping a coin, then rolling a die - Stuck on Part (c)

Part (a). Using the negative binomial distribution, write an expression for the probability that exactly $k$ flips of a coin are needed to get $m$ heads, where $k \ge m \ge 1$. My answer: $P(H)=\frac{1}{2}$ and $P(T)=1-P(H)=\frac{1}{2}$ $\therefore…
Nicko
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What is the distribution of the stopping time for Brownian motion with two barriers?

The distribution for the stopping time of Brownian motion with one barrier is well known. There is also the formula for the expectation AB, where A and -B are the barriers, A,B bigger than 0.
Tristram de Piro
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What type of beta distribution is this this?

I'm seeing a distribution where the pdf $F(x)$ for random variable $x$ is like this: $$ F(x) = (bx)^a + o(x^a)$$ where $a>0$ and $b>0$. EDIT: For context, this distribution appears near the beginning of this paper:…
underdog987
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