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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Does kurtosis measure center?

Some have stated that kurtosis is the "movement of probability mass from the “shoulders” of a distribution into its center and tails" where "center" is defined as the range between $\mu \pm \sigma$. I was trying to find a proof for this but was…
BigBendRegion
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Analytical expression of Pearson's correlation

I do not understand the notation of Spearman's correlation in the article of B Schweizer, EF Wolff - The annals of statistics, 1981 - JSTOR given by $\rho = \frac{1}{\sigma_X \sigma_Y}\int_{R^2}( F_{X,Y}(x,y) - F_X(x)F_Y(y)) dx dy$ Whn I use…
HammerPower
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Uniform distribution dependent on another uniform distribution

I was asked this question on an interview and had trouble so I'm turning here after the fact for help understanding what I should have done. Suppose we choose $x$ uniformly on $[0,1]$. Now we choose $y$ uniformly on $[x,1]$. What's the distribution…
Leo 254
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Average distance between two outputs of a probability density function with real numbers as output?

Given a 1-dimensional PDF with real numbers as output I need to find the average of distances $|a-b|$ between two outputs of such PDF. What I know is that the integral of the PDF must be 1 from -infinity to +infinity, and I somehow need to use an…
Garmekain
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Probability density functions C

Please excuse my use of images The answer to this is that no the first function cannot be a pdf, but the second one can with a restriction. All explanations I try to look just confuse me further. Why for the first function since we have…
Allan
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Probability Distribution - Picking marbles

There are 6 black marbles and 7 white marbles in the bag. Without replacing the marbles, we repeatedly pick a marbles until it is a white one. Call X: the number of marbles until we can pick a white marble. What is the probability distribution of…
Math. H
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Statistics and Probabilities

In a list of 20 individuals who volunteered to supply blood, when it is needes for transfusion has 15 individuals of type B blood and 3 individuals are selected randomly from the list, what is the probability that: a)all three will be type B, b) 2…
Chris Gerou
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Let $(X,Y)$ be a bivariate discrete R.V. with joint pmf $p(x,y)=1/{{m+1 \choose 2}}$

Let $(X,Y)$ be a bivariate discrete R.V. with joint pmf $$p(x,y)=\begin{cases} \frac{1}{{m+1 \choose 2}} \text{if $y=1,2 \ldots,x$ & $x=1,2,\ldots,m$} \\ 0 \ \text{otherwise} \end{cases}$$ for a given positive integer $(m>1)$.Find $E(X)$ from the…
user321656
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two function of two random variables

Supposed we are given a random variable $X$, whose probability density function is: $$ f_X(x)=\begin{cases} λ \exp⁡(-λx), & x≥0 \\ 0, & x<0. \end{cases} $$ We wish to find an invertible function $g$, such that $Y=g(X)$ is uniformly distributed on…
Deepsea234
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conditional pdf with independent identically distributed standard normal random variables.

Random variables X and Y are independent identically distributed standard normal random variables. Consider random variables U=aX+bY and V=aX-bY, where a and b some fixed numbers and a^2 +b^2 =1. a. Determine the joint pdf fuv, using the Jacobian…
Deepsea234
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Computing a transformation of a bivariate random variable

Given the bivariate random variable (X,Y) with PDF: $ \begin{cases} \frac{2}{7}(2x+5y) & 0
MilTom
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Probability of radioactive decay of a non-uniform system

It is given that the probability that one among two radioactive atoms will decay in an interval $x,x+dx$ and another one will decay in a time interval $y+dy$ is given by the following expression: $$Ne^{-y\alpha-x\beta-\gamma\sqrt{xy}}dydx$$ where…
Spoilt Milk
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Probability of radioactive decay

It is given that the probability that one among two radioactive atoms will decay in an interval $x,x+dx$ and another one will decay in a time interval $y+dy$ is given by the following expression: $$Ne^{-y\alpha-x\beta-\gamma\sqrt{xy}}dydx$$ where…
Spoilt Milk
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Continuous random variable and the normal distribution

How are we going to know that a continuous random variable is a normal random variable? The definition I believe for a continuous r.v. to be a normal r.v. is that it's probability density function must be the pdf of the normal distribution. How are…
Isaac Newton
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How do you find the probability of $P(X\le23|X>13)$ if any?

Let X be a continuous rv with PDF $$Fx(X) =\begin{cases}4x^3 & 0
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