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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Bernoulli distribution with non integer number of trials

Can we generalise the Binomial distribution for a non-integer number of Bernoulli trials?
Dionysios Georgiadis
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SD of a bernoulli trial?

Why nothing is mentioned about the standard deviation of a Bernoulli trial ? Does it even make sense if I try to visualize it ?
Oleg
  • 499
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Joint probability density function, unit circle?

So I am given $$ f_{X,Y}(x,y) =\begin{cases}\frac{1}{\pi}&\mathrm{\ if \ } x^2+y^2\le1\\ 0&\mathrm{\ otherwise\ }\end{cases} $$ And am asked to find joint probability density function for $X+Y$. I'm assuming that I must use $$ f_{X+Y}(z)=\int…
Bacon
  • 63
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A nearest-neighbor problem for dependent absolute differences

I've stumbled on an interesting problem that I hope someone can help with. First, declarations: (a) this is not (cruel) homework, but arose in behavioral modeling; (b) I've spent a lot of time searching this forum and found nothing that I can…
Kirbs
  • 31
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Finding PDF of sum of 2 uniform random variables

I need help understanding the question and its solution below. Suppose that X is uniformly distributed in [0,a] and Y is uniformly distributed in [0,b], $0 < a \le b$, and that X and Y are independent. Find the PDF of $Z=X+Y$. The solution is…
Rayne
  • 331
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Uniform distribution of survivor evaluated at lifetime

The question is: Let $T$ be a continuous random variable with survivor function $S$ defined on the interval $[0, \omega]$. Now consider the random variable $S(T)$, the survivor function evaluated at the unknown lifetime value $T$. Show that $S(T)$…
Liam Williams
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Alaskan Bears Probability

One of the popular tourist attractions in Alaska is watching black bears catch salmon swimming upstream to spawn. Not all “black” bears are black, though— some are tan-colored. Suppose that six black bears and three tan-colored bears are working the…
kingston
  • 41
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Prove an interesting property of pdf moments?

I am examining properties of mass moments of probability densities: $$ m_{i}\equiv\int_{-\infty}^{\infty}x^{i}f\left(x\right)dx $$ Define a $\,n\times n\,$ covariance of the first $\,n\,$ moments: $$…
Jerry Guern
  • 2,662
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Conditional probability distribution with geometric random variables

Let X and Y are independent random variables following geometric distribution with parameter p. Find the distribution of X given that X + Y = n. I made it this expression... $$P\{X =i|X+Y=n\}=\frac{(1-p)^2p^2}{P(X+Y=n)}$$ I do not know how to…
user50098
  • 187
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Calculating Probability (P) given Z bounds.

I need to program a simple Probability calculation function for any given Z boundaries (Area P under the normal distribution curve): I know we can use the The Z table, but I want to actually calculate it - I found that the actual calculation…
Shlomi Hassid
  • 91
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Finding the pdf of particular element.

Let $Y_2$ denote the second smallest item of a random sample of size $n$ from a distribution of the continuous type that has $\text{cdf }F(x)$ and $\text{pdf }f(x) = F'(x)$. Find the limiting distribution of $Wn = nF(Y_2)$. I am not sure…
lord12
  • 1,958
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Waiting time of Poisson process follows Gamma distribution

Suppose that events occur according to a Poisson process with rate $\lambda$, so that for every $t > 0$, the number of occurrences $N(t)$ in the time interval $[0,t]$ has a Poisson distribution with parameter $\lambda t$. Let $T_n$ be the waiting…
jake
  • 33
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Will someone please explain multivariate normal distributions with a real-life example?

I understand a concept best when I see it being applied in the real world.
moonman239
  • 553
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How to get uniform distribution with two dice rolls?

The sum of two dice rolls will not have uniform distribution. Never realized... Is there an easy way to cheat? Will this work? 1st die roll, 1-6... 2nd die roll, if 1-3, add 0 to first die, if 4-6, add 6 to first die. Is this sum uniformly…
Shing Lau
  • 41
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Order statistics: does distribution of sum of two of them uniquely determine parent distribution?

Let $X_1, X_2, \ldots, X_n$ be a sequence of i.i.d. r.v. with bounded range (say, the interval [0,1]), with cdf $F$. Let $Y_1 \geq Y_2, \ldots, \geq Y_n$ be the corresponding order statistics. My question is very simple: Is the distribution of…
Claudio Gentile
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