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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The distribution of i.i.d. normal random variables removed for their median

$X_1$, $X_2$,...,$X_n$ are $n$ i.i.d. normal random variables. $Y$ is the median of these variables. I am asking if for a finite even number $n$, $X_1-Y$, $X_2-Y$, ..., $X_n-Y$ are i.i.d. symmetric distributed random variables, so that the…
Kefu Liao
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Is there a distribution like this?

Is there a distribution like in the picture? It don't need to be the same, but like the idea (postive mean, negative next to mean and zero against $-\infty$ and $\infty$).
user93287
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The Distribution of the Linear Interpolation of Normally Sampled Points

This is mostly me reasking this question because I believe I have an alternative approach to a similar idea, whereas this seems to be adding some kind of discretization instead. Let $(X_i)_{i=0,\cdots,n}$ be i.i.d normal standard normal variables.…
Thomas Pluck
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Convergence to normal distribution.

Let us suppose we have an infinite number if Bernoulli variables that can take one of two values: $-1,1$, with equal probability. Then their sum converges to a normal probability distribution. What about variables that can take three values,…
Ryan Hendricks
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Mean and variance of Cauchy-like distribution

$P(x)= \frac{b}{|x|^{2.2} + 1}$ Looking at this distribution function, is there a simple integration technique (beyond residues in complex analysis) that gives us the value of b through normalization? Secondly, for the mean and variances, I can…
djorkaeff
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How to show that there is only one possible distribution for $X$ with variance $\frac{1}{4}$, where $X \in [0,1]$.

Let $X$ be an r.v. (discrete or continuous) such that $0 ≤ X ≤ 1$ always holds. Let $μ = \mathbb{E}(X)$. Show that $$a.) \ Var(X) \leq \mu - \mu^2 \leq \frac{1}{4} \\ b.) \ \textrm{ Show that there is only one possible distribution for }X \textrm{…
TopoSet32
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Convergence to a non-degenerate distribution

If we have iid observations $\mathbf {(X_1,Y_1),(X_2,Y_2),\dots}$ from bivariate distribution $G$ supported on unit disc $\mathbf {[(x,y): 0 \le (x^2,y^2) \le 1]}$. Suppose that distribution has a continuous density $\mathbf {g(x,y)}$ with…
user87455
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Is there a family of probability distributions for ...?

Is there a family of probability distributions for $P(x|y,n)=\frac{\Gamma(n+y)}{\Gamma(n)\Gamma(y)}(x+1)^{-n-y}x^{y-1}$ ? $n>0$ and $y>0$ Has it an explicit expression for the CDF?
jss
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Translating small differences in sums of powers of numbers into distance measure

I am currently thinking about the following problem, which seems to be rather elementary, but I was unable to find or come up with a satisfactory solution. Assume that there are two sorted sequences of numbers, $0 \leq \lambda_1 \leq ... \leq…
Herimon
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Max of n normal random variates

Suppose $X_1, X_2, \ldots, X_n$ are iid distributed as $N(0,1)$. Define: $$ Y=1+\max _i\left|X_i\right| $$ I want the distribution (CDF) of $Y$. My attempt: Let $V=\max _i\left|X_i\right|$ Since $X_i \sim N(0,1)$, the distribution of…
AgnostMystic
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Does the probability distribution associated with this pdf have a name?

The pdf is $$f(x)=\frac{ab^a}{(x+b)^{a+1}}$$ for $x\geq0$ and some parameters $a,b$. I've come across it a couple of times in study material for the actuarial exams.
crf
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Probability Distribution for Product of two Random Numbers?

If I multiply two random numbers from 1 to 10 together I will get an outcome from 1 to 100. Over a large enough sample size the outcomes will tend to cluster closer to 1 than to 100 (only 21 of the 100 possible outcomes are greater than 50, for…
user88429
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Finding the initial distribution of a particle

Fix $n ≥ 4$. Suppose there is a particle that moves randomly on the number line, but never leaves the set $\{1, 2, . . . , n\}$. The initial probability distribution of the particle is $π$ i.e., the probability that particle is in location $i$ is…
Tapi
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Using Poisson distribution to win a bet that a theater wont be N% full by the time the movie starts

Then just from a brute force computation, I found that the largest value of $N$ needs to be 99 since any value greater than 99 is greater than 0.5. Is that correct? or is there another way to solve without brute force computation?
user8290579
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