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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Density of probability and Distribution function, how to turn one into the other

I know that to know the Distribution function I got to integrate the Density function from "-oo" to "x", but how to do the inverse?
user2993157
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How to choose between poisson and binomial distributions

I don't get this thing... I know that binomial distribution is used to know the probability of a X v.a. that sounds like this: X = "the probability of having 4 blue balls doing 10 extraction from a chest containing 7 blue and 40 white", and I know…
user2993157
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continuous distribution with change of variable

I'm trying to do this question: If $X$ is a continuous random variable with a mean of 2 and a variance of 4, find the mean and variance of $Y$, where $Y=\log{X}$. I know how to find the expectation and variance from a pdf, but I don't understand how…
George
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PDF of $f(x)=1/\sin(x)$?

What is the probability density function (PDF) of $f(x)=1/\sin(x)$ when $x$ is uniformly distributed in $(0,90)$? $f(x)=\sin(x)$ has a known PDF, which has the form $2(\pi\sqrt{1-\sin(x)^2})^{-1}$, but I cannot find the PDF for $1/\sin(x)$. The…
Sebastian
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Determine $f(y_1, y_2)$ precisely.

Context of the problem: Continuous bivariate random variable $(Y_1, Y_2)$ has the uniform density $f(y_1, y_2)$ on support S = $(y_1, y_2) \leq 1-y_1^2, y_1 \leq 0, y_2 \leq 0$. Thus, $f(y_1, y_2)$ has a positive constant value on S and value 0…
Nick
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Probability Distribution Table of random Variable X

I am having issues with constructing a probability distribution table of a random variable x. Here is the question: According to recent data, 16.1% of motorists are uninsured. Suppose that 2 motorists are selected at random. Let x denote the number…
user104960
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How can I determine the parameters of a beta distribution given a histogram?

I have a histogram, and I want to estimate the parameters of the underlying distribution. Here is the data I've taken from the graph: $$ \begin{array}{c|lcr} \text{Interval} & \text{Count}\\ \hline 0-.70 & 0\\ .70-.75 & 1\\ .75-.80 & 21\\ .80-.85 &…
PhiNotPi
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Gamma Distribution vs Convolution of 2 Exponential Random Variables.

If X and Y are 2 independent random variables with Exponential($\lambda$) distributions, my understanding is that their convolution (Z = X + Y) is given by: $f_Z(z) = -\lambda ze^{-\lambda z}$ The convolution formula is supposed to be: $f_Z(z) =…
EggHead
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cdf of $X/(X+Y)$, where $X$ and $Y$ are i.i.d. uniform

$X$ and $Y$ are i.i.d. uniform on $[0,1]$. I am asked to find the cdf of $R=\frac{X}{X+Y}$. I tried to use the auxiliary variable $S=X+Y$, find the joint pdf and then marginalize, but I am not able to find the support of $(R,S)$. How would you go to…
user70645
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Probability distribution for the number of points in a D-sphere when uniformly sampling a D-dimensional space

I have a D-dimensional space of volume V, and I uniformly sample it $P$ times by randomly positioning points / throwing darts / etc. I also randomly position some number, $N$, of non-overlapping $D$-spheres, for the same value $D$ as the dimension…
B.M.
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Determining which Probability Distrubitive Function to use

I have two questions that I am to solve as practice. I am having difficulties with determining which probability function to use. The firstquestion is: Todd decides to keep buying a lottery ticket each week until he has 4 winners (of some prize).…
0xFF
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Does this figure represent a cumulative distribution function?

Is this a c.d.f.? I have no problem for random variable $X$ at $-\infty
Silent
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Conditional probability with and without replacement

A sample of size $r$ is taken from a population of $n$ elements. Find the probability that none of the $N$ prescribed elements will be included in the sample, assuming the sampling to be a) without b) with replacement . Compare the numerical value…
Brian makenzy
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Is it right way to calculate pdf

Which of these is the right way to calculate pmf. P(X=0) = (5/6)^4 or P(X=0) = (number of ways of choosing 4 out of 25)/ (number of ways of choosing 4 from 30)
user30438
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Approximation of Binomial distribution with Poisson

I have to prove $\sup|P_{n}(k)-\pi_{\lambda}(k)| \leq \frac{\lambda^2}{n}$ where $P_{n}(k)$ is distribution of Binomial RV with parameters $(n, \frac{\lambda}{n})$ and $\pi_{\lambda}(k)$ is Poisson with parameter $\lambda$. I've shown that if…
sigma.z.1980
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