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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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Almost surely positive.

Hello i have a little question about probability. I have a function defined on $\mathbb{R}$ as follows,$f(x)=\frac{4x}{(1+x^2)^3}\mathbb{1}_{x>0} $ I have to show that this is the density of an r.v $X$ and that $X>0$ almost surely. Assuming i've…
vadkoslo
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Flattening the distribution of scores in a game to provide a difficulty

I have many routes a player can take in a game I'm making. Each route awards them a specific score (ranging from 4 to 31, but mostly concentrated around 8 and 11) and I need to decide which difficulty challenge to present the player with in order to…
hopperelec
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Removing an element from a probability distribution table

I have the following probability distribution table: [0.2, 0.3, 0.5] I will then set the probability for event 1 to 0. [0, 0.3, 0.5] Now the question is what should the probabilities of the other events be, when everything has to add up to 1. I'm…
user2997204
  • 139
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Non symmetric urn and balls problem.

Consider an urn containing $N$ balls, of which m are white and $N - m$ are black. Balls are randomly selected from the urn according to the following rule: If a black balls is selected, it is "observed" and the it is returned to the urn. If a white…
Mario
  • 87
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The $n^\text{th}$ moment of $p(x=k)=\dfrac{pq^k}{1-q^{N+1}}$

Find the $n^\text{th}$ moment of $p(x=k)=\dfrac{pq^k}{1-q^{N+1}}$, $k=0,1,2,\ldots,N$ , $0\lt p\lt 1$ and $q=1-p$. My approach is $$M_x(t)=\sum e^{xt}\cdot p(x)=\frac{p}{1-q^{N+1}} \cdot \sum_{x=0}^N e^{tx}q^x$$ Now,…
Vikas Sharma
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Does this probability distribution have a standard name?

Let $n\geq 0$ be a natural number. Consider the probability distribution on $\{0,\ldots,n\}$ whose probability mass function is given by $$ \mathbb{P}(X=k) := \binom{k-\frac{1}{2}}{k}\binom{n-k-\frac{1}{2}}{n-k} $$ where as usual $\binom{x}{k} :=…
Gro-Tsen
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Help with creating Pareto distribution given a limited set of data.

I am trying to calculate/create a Pareto distribution with basically only knowing the $x$ and $y$-axis of the chart. The maximum set of data would be $200,000$ with the minimum being $1$. The amount of users would be $226,000$. In short, I am trying…
AZWoody
  • 21
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$ P(|\mathcal{N}(0,1)| >k) \leq e^{-k}$

$X \sim \mathcal{N}(0,1)$ $ k \geq 2$ We want to prove that $ P(|X| >k) \leq e^{-k}$ My attempt : $ \begin{align*} P(|X| >k) & =P( e^{ |X| } > e^k ) \\ &\leq e^{-k} E( e^{|X|} ) \\ &= e^{-k} \int_{0}^{ \infty} \dfrac{2}{ \sqrt{2 \pi} }e^{-t}…
zestiria
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Are there any named probability distribution of $x$ proportional to $e^{-\alpha x}(1-e^{-x})^{\beta -1}$?

Are there any named probability distribution of $x$ like: $$ Pr(x)=\frac{\Gamma(\alpha+\beta)} {\Gamma(\alpha)\Gamma(\beta)} e^{-\alpha x}(1-e^{-x})^{\beta -1} $$ where $x\in(0,\infty), \alpha>0,\beta >0$. In particular I would like to have an…
jss
  • 269
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Expectation values in directional statistics

In the context of Variational Bayesian Inference I am facing the following problem: Let $\alpha$ follow a "von Mises" distribution with mean $\mu$ and concentration $\kappa$. Does there exist a formula for the calculation of the expectation values…
Matthias
  • 21
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Finding an MGF of discrete variable given some moments

Problem statement: Let $X$ be a discrete random variable. Given that $E(X) = 0$, $E(X^2) = 2$ and $E(X^4) = 4$, find the moment-generating function (MGF) for $X$. Now I know that the general formula for the MGF is $M_X(t) = \sum_{i = 0}^{\infty}…
RedDocMD
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Random Variable Transformation With Dirac delta function

Consider $f_X(x) = 1/2+x$ where $0
WaterDrop
  • 600
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How to find the probability of one die roll being higher than a second die roll?

And the catch is the first die has $x$ sides, while the second die has $y$ sides, where $x\neq y$ I had this figured out several years ago, but apparently have forgotten both the answer and too much math since then to either work it out or figure it…
Darth Android
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$Z = \min(X,Y) \sim$ Geometric$(\lambda\mu)$ provided that $X \sim$ Geometric($\lambda$) and $Y \sim$ Geometric($\mu$)

Let $X, Y$ be independent geometric r.v.'s with paramaters $\lambda$ and $\mu$. Let $Z = \min(X,Y)$ and show that $Z \sim$ Geometric$(\lambda\mu)$. I have seen 5 posts of the same question on this website and yet I cannot get the right answer. This…
Vicky
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How many times must I repeat a trial to have confidence in a true result?

How can I calculate the number of times I need to repeat an independent test with a probability (p) in order to have 99% confidence that I will have at least 1 true result? Example: I have a task that has a 20% chance of succeeding (p=0.2). How many…
Matt
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