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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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Fractional part of sum of two uniforms

Can we prove that {U1+U2} (fractional part of sum of two uniforms(0,1) ) is also uniformly distributed in [0,1]?
chandler
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How can I find the CDF and PDF of $Y$?

Problem Let $X$ be a $\operatorname{Uniform}(0,1)$ random variable, and let $Y=e^{-X}$. Find the CDF of $Y$. Find the PDF of $Y$. Find $\mathbb E[Y]$. My problem If I solve for the range of $y$ I get $\left(1, \frac 1e \right)$, but because $Y$ is…
Jonathan Yoder
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What kind of distribution is this (PDF bounded within interval)?

Please excuse my naïvety in this matter, but what kind of distribution is this, where the max/min is bounded by a definite interval (in this case, $[0,3]$ )? I can see the (elegant) accepted answer is a triple intergal, but is it possible to define…
martin
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Probability Distribution problem.

We need to divide a line segments into two parts by selecting a point at random. Then we have to find the probability that the length of the larger segment is at least 3 times the shorter. My take to the problem : Considering a line segment of unit…
User9523
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Conditional expectation and variance.

We are given that $\operatorname E(Y|x)$ is linear in $x$ and $\operatorname{Var}(Y|x)$ is a constant. We need to prove that $\operatorname{Var}(Y|x) = (\operatorname{Var}(y))^{2} (1-r)^{2}$ where $r$ is the correlation coefficient. I tried…
User9523
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marginal density valid probability density function

fX,Y (x, y) = 24xy, 0 < x < 1, 0 < y < 1, 0 < x + y < 1 (a) Is fX,Y (x, y) a valid probability density function? using the integral 1→0 12x(1 − x)^2dx → 12x^3 − 24x^2 + 12xdx = 3-8+6 =1 correct?
kurtk3
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What is the generalization of the Inverse-Chi-Square distribution when there is extra known variance?

If I have a normal distribution, the posterior for the variance is the inverse Chi-square distribution assuming the same is used as a conjugate prior. But what if my data has extra noise added so that the observed sample variance is the sum of the…
David Johnston
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What distribution is this borne out by real data?

Hi I am looking at submission data - the length of time it takes for someone to complete a flow which involves submitting an item of content. I am getting the following distributions. Two quick questions: What best describes the frequency…
user7289
  • 111
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Joint distribution of positive weights with sum unity and an equality constraint.

Suppose I have a vector of positive weights $a=(a_1, a_2, a_3, a_4)'$ such that $a_2=a_3$ and $a_1+a_2+a_3+a_4=1$. Is there any way to construct a joint sampling distribution for $a$ with a compact functional form ? P.S. The context of this problem…
Dey
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Let $X$ be a random variable with probability density function $f$. Prove that the probability distribution function of $X$ is non-decreasing

Can anyone please help me with this random variable question I've stumbled across. Recall from calculus that a function $h$ is called non-decreasing if $x \le y$ implies $h(x) \le h(y)$, for every $x, y \in \mathop{\mathrm{dom}} h$. Q1a) Let $X$ be…
Ricky Rozay
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Calculate the p.m.f. of a non-monotonous function of a random variable

I've been trying to prove the following and I'm really stuck. Consider $N\sim \mathrm{Geometric}\left(p\right)$, and let $X=(-1)^N$. Show that the probability mass function of $X$ is given by $$ p_X\left(k\right) = \begin{cases} \frac{1}{2-p},…
MrPoisson
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A die is cast $3$ independent times, let $Y = \max(X_1,X_2,X_3,)$...

A die is cast $3$ independent times. Let $X_i$ be the random variable representing the number on the face appearing at the $i$th cast. Let $Y$ be the random variable defined by $Y = \max(X_1,X_2,X_3)$. Find the C.D.F and P.D.F of $Y$. Answer key…
George
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What is the "Cumulative Distribution of the magnitude of the N-dimensional standard gaussian"

I am confused by this line from a paper: "Let $F_1(x)$ be the cumulative distribution of the magnitude of an $n$−dimensional standard Gaussian random variable and $F_2(x)$ be the cumulative distribution of the magnitude of a random point in a…
Andy Yao
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mean of an arbitrary distribution

Is it possible to find the mean or center of a continuous arbitrary distribution. Assuming that an object O is arbitrarily distributed within arbitrary shape, can we find its mean or center geometrically or by any other method if the distribution is…
shaikh
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