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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Binomial probabilities

Okay, so here is probably the easiest question ever on this website. A question on binomial distribution. In a city, the percentage of left-handed women is 16% and the percentage of left-handed men is 22%. A random sample of five men and five women…
9765712
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Finding a joint probability density function given marginal probability density functions

X and Y are independent random variables with the following PDFs: $f_{x}(x) = \begin{cases} (1/3)e^{-x/3}, & x \geq\text{ 0} \\ 0, & \text{otherwise} \end{cases}$ $f_{y}(y) = \begin{cases} (1/2)e^{-y/2}, & y \geq\text{ 0} \\ 0, &…
Swamp G
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Finding out the probability distribution of numbers from -3 to 3

I am really able to solve problems with the help of all the volunteers here. a big thanks to every one.. Please explain this problem.. A random variable 'X' takes the values -3,-2,-1,0,1,2,3. Such that P(X=0) = P(X<0) = P(X>0) and P(X=-3) =…
Ganesh Vellanki
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What is the probability density function of $g(S) =S/2$ for a triangle pdf

Say we have the following "triangle" probability density function: $ p_{S}(s) = \left\{ \begin{array}{lr} s & : s \in[0,1]\\ 2-s & : s \in [1,2]\\ 0 & o.w. \end{array} \right. $ I want to sketch or write down a…
Charlie Parker
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Actuary P/1 Exam Question

I was taking a practice exam and I don't understand a step in one of the solutions to the problem. I understand every part except why $f(y^{0.5})=8(y^{0.5})^{-3}$ If someone could help explain that to me it would be very helpful. Edit: Just to be…
Robert Maggio
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Passing thresholds with uniform random variables

I have encountered a challenging task: I have a bunch of uniform random variables "trying" to pass a certain threshold, and another bunch trying to pass a different threshold, and I need to estimate the difference of the number of successes. I'll…
Bach
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What is expected color of an object?

There is a set of n objects $\{a_1,a_2,\ldots,a_n\}$ each having color $c_1,c_2,\ldots,c_n\}$ respectively. Now a random subset of this objects is selected and painted with some random color from set $\{d_1,d_2,\ldots,d_k\}$. What is the expected…
Abhishek Goyal
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Computing the density function of max of two items.

Let $X$ be exponentially distributed with mean $3$. Then how do we compute the density function of $max\{X,2\}$?
Matt
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Poisson process: nth jump from expectation of interarrival time

The interarrival time for a poisson process is given as $ \Bbb E[T_i] = 1/\lambda $ How can I compute the arrival time for the $nth$ jump from this. Surely its not equal to $n/\lambda$ ?
takeshi kovacs
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a 12-side dice with a lot of players probability problem

One million players participate in a game that has 10 levels. At first, all players are at level 1. At the end of each turn, each player rolls a twelve-sided die, numbered 1 to 12. Player advance a level if he gets a higher number of its current…
JeanClaudeDaudin
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Bivariate Transformation

Why can I not let $V=X$ in this transformation as opposed to $V=Y$? I have tried it with $V=X$ and i get a different joint pdf.
usainlightning
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Expectation of minimum set of i.i.d random stopping times with the same distribution

What is the expectation of the minimum set of n i.i.d random stopping times? is it \frac{T}{n}
user156391
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Reability of any CDF in Excel based on the binomial one as Cumfreq does.

I'm trying to get my own excel sheet to calculate the confidence limits or belts. I'm interesting in apply it to the Two Components Extreme Values (TCEV) Distribution for Flood Frequency Analysis and the Gumbel (Tipe I) distribution. But for a…
JOSEPH_GRANADA
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Hypergeometric Distribution Confusion

I'm having trouble understand the part of the pmf for the Hypergeometric Distribution highlighted in green: $$\Pr[X = k] = \frac{\dbinom{m}{k}\!\!\color{green}{\dbinom{N-m}{n-k}}}{\dbinom{N}{n}}$$ If you have chosen k "Type 1" objects from a…
usainlightning
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Calculate the probability that out of $5$ randomly chosen claims $3$ are of the size $£5,000$

A very crude model for the distribution of claim size, $X$, in a particular situation represents $X$ as a discrete random variable, which takes the values $£5,000, £10,000,$ and $£20,000$ with probabilities $0.4, 0.5,$ and $0.1$…
Jaguardo
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