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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Looking for a distribution to describe 2D "lines"

I have a 2D surface endowed with line segments, i.e. the function contains sparsely distributed segments in which there is high correlation between adjacent points in some direction, and the rest of the function is zero. I'm looking for a vector…
yoki
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Pdf of variable as combination of two random variables with exponential distribution

If $X$ and $Y$ are independent and exponentially distributed, which is the pdf of $Z$? Where $Z$ is given by \begin{equation} Z = \frac{X}{1+Y} \end{equation} I read answer to this post: $X,Y$ are independent exponentially distributed then what is…
smtux
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Calculating Chi-square probability with $X^2$ and degrees of freedom

How do I calculate the probability (%) for chi square test using $X^2$ value and DoF as inputs? Im trying to create a C++ program to calculate chi square tests with very high DoF, so I cannot use the table to check the probability. I have already…
user3439124
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Standard deviation and Mean

Scores on a test follow normal distribution with mean of 460 and SD of 100. If all students in class of 41 attend the test what is probability that the given class will obtain a mean score of above 589.93? I can work out the Z score but am…
Elise
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Find the distribution of $\sqrt{X^2+Y^2}$ where X and Y are normally distributed.

Find the distribution of $\sqrt{X^2+Y^2}$ where $X$ and $Y$ are independent normally distributed $\mathcal{N}(0,1)$. What is the best way to go about this? I tried finding the distribution of $X^2$ and $Y^2$ and then adding the two distributions,…
guest10923
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Deriving a distribution from the line generated from a point in a uniformly distributed circle and its origin

Let $a,r>0$ be two fixed numbers. A random point $(X,Y)$ is uniformly distributed over the circle {$(x,y) : x^2+(y-a)^2 = r^2$} with the centre of the circle at $(0,a)$. A line is drawn through $(X,Y)$ and $(0,a)$ and the line intersects the $x$…
YellowPillow
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Creating a categorical probability distribution based on scores

I am looking for a method to create a categorical distribution from a set of possible options with an associated known score. Example: In a game where there are 4 options each rewarding the following a scores Option 1: 1000 points Option 2: 675…
user1417861
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Marginal density functions

Given a disc with center at origin and radius one, where $$f(x,y) = 1/\pi$$ $$\sqrt{x^2+y^2} =1$$ the marginal density function of $X$ is $$2/π * \sqrt{1-x^2}$$ Can the marginal density function of $Y$ be extrapolated without calculation and taken…
Edward
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Cauchy distribution

For a given value of the location parameter say it is 0. Why does the median equal the location parameter. I'm slightly confused by what the location parameter actually represents? Any help would be much appreciated.
Sal1
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How does one in general decide to use a binomial distribution vs a Poisson distribution?

I saw the following problem and thought Poisson would be the correct distribution, but the solution manual says otherwise. My textbook says an event is rare if the number of trials is at least 50, while $np \leq 5$. Here $np = 20*.05 = 1 \leq 5$.…
Joseph DiNatale
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Adjusting mean value of the beta distribution

I'm reading a paper[1] that performs a simulation with task graphs. The paper uses beta distribution to assign weights for the nodes in the graph. The graph is already known with certain weights in it, but before simulation happens weight of the…
mcsim
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Parameters of extreme values distribution for a family of distributions

My random variable is defined as $X=\max({x_1,...x_n})$, with $n$ very large. The $x_i$ are iid random variables following a Binomial distribution with with $k$ trials and success-probability $p$. $k$ can be safely assumed to be large enough to…
CupiDio
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Joint Distribution: Define new random varaible

im working on practice problems from the book and i have come across a question that i do not understand... The joint probability distribution of X and Y is shown in the table: X Y 1 2 3 2 0.10 0.15 0.20 4 0.30 0.15 0.10 a)Define the…
Jovis13
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Ratio of exponential distributions

Stuck on this question, and I have no idea how to proceed: Let $X$ have the probability density $f_{X}(x)=\lambda e^{-\lambda x}, \;\; x>0$ and let $Y$ have the probability density $f_{Y}(y)=\lambda e^{-\lambda x},\;\; y>0.$ Find the probability…
George1811
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how to calculate marginal distribution of continuous random variables

The two continuous random variables X and Y are jointly distributed as $f(x,y) = 24x^2y(1-x)$ for both x and y are greater than and equal to 0 and less than equal to 1 and 0 elsewhere. calculate the marginal distributions of X and Y Did you mean…
user215453
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