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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Probability independence calculation

Two random variables, $X$ and $Y$ , have the joint distribution $P(x, y)$, $$ \begin{array}{cc|cc} && x\\ && 0 & 1\\ \hline y & 0 &0.5 &0.2\\ &1 &0.2& 0.1 \end{array}$$ Are $X$ and $Y$ independent? Explain. Are $(X + Y )$ and…
Satyaki Chatterjee
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How can one compute the cumulative distribution function of $\max (E -6,0)$, where $E$ is uniformly distributed?

Let $E$ be uniformly distributed between $0$ and $10$. The cumulative distribution function of $\max(E-6,0)$ is: $$F(x) = \left\{ \begin{array}{ll} 0 & \mbox{if } x < 0 \\ \frac{6+x}{10} & \mbox{if } 0 \leq x \leq 4 \\ 1 & \mbox{if }…
Max Muller
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How to integrate a normal density

$Y\sim \mathcal{N}(\mu,\sigma^2)$. And $Y=\log X$ To find the probability density function of $Y$ and median of $Y$. How I proceed: $Y=\log X$ $X=e^Y$ Using distribution function technique $F(x)=\mathbb{P}(e^y\leq x)=\mathbb{P}(y\leq\log x)$ Now…
demon
  • 125
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To find the conditional distribution of exponential variates.

Let X and Y be independent random variable each having exponential distribution with parameter lambda. Then the conditional distribution X given X+Y=1 is?? How I proceeded was: X=r ,Y=1-r And accordingly I wrote the exponential distribution. But I…
demon
  • 125
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$X,Y,Z$ are iid random variables $\implies$ $X-Y$ are $Y-Z$ are independent

Let $X,Y,Z$ be independently and identically distributed random variables. Is it true in general that $X-Y$ and $Y-Z$ are independent$?$ Is there any counter example$?$
user469680
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simple binomial distribution question

this is a simple example from a statistics textbook that i am a little confused about. why is the last binomial coefficient 9 choose 7? shouldn't it just be 1? i'm sure that i'm overlooking something simple but i haven't been able to figure it…
user268537
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To find the probability of uniform variates.

If $X$ and $Y$ are independent and both follows $\operatorname{Uniform}(0,1)$. Find $P(|X-Y|)\ge1/2)$ Here we are given the difference of $2$ uniform variates...But I think the density difference of $2$ uniform variates is of no use here. Here we…
demon
  • 125
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Find the probability distribution based on half-Gaussian and Rayleigh

Problem Suppose random variables $X$ and $Y$ are independent, and $X$ has a half-Gaussian distribution with $\mu=0$ and $\sigma^2=1$, $Y$ has a Rayleigh distribution with unknown $b$. Then what is the distribution of $Z=XY$ What I have Done This…
Mr.Robot
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Normal Distribution Problem Involving Events

Suppose that X~(2,9) and calculate the probability of the following events: a) x^2+x-2 > 0; b) abs(x-2) < 1
Sam202
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Finding the Mean of a Probability Distribution

Let $X$ be a random variable with the following probability distribution: $$x: \{−3;6;9\}$$ $$f(x): \{\frac16;\frac12;\frac13\}$$ I'm asked to find $\mu g(X)$, where $g(X) = (2X+1)^2$. The mean i'm looking is expressed as: Mean $g(x) = E[g(x)] =…
Sam202
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How do I find the joint pdf of the joint distribution X, Y, Z

Six cards are to be drawn from an ordinary deck of cards. $X$ is the number of low ($1$-$5$) black suited cards drawn $Y$ is the number of high ($6$-$10$) red suited cards drawn $Z$ is the number of face cards drawn. What is the joint pdf of $X, Y,…
Yuumi
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Is $EXX^2 = EX^3$?

Let $X$ (respectively, $X^2$) be a random variable with a given probability density function $f_X$ (respectively, $f_{X^2}$). Is the following statement true: $$EXX^2 = EX^3 = \int_{-\infty}^{\infty}x f_{X^2}\left(x\right) f_X\left( x \right)\;dx =…
SlowerPhoton
  • 799
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Can weak convergence of distribution function imply the convergence of left limit?

If $F_n$ and $F$ are distribution functions, and $F_n$ weakly converges to $F$. Then we know that $F_n(x) \rightarrow F(x)$ when $x$ is the continuous point of $F$. I want to ask: can we deduce that $F_n(x-) \rightarrow F(x-)$ for every $x$? And…
Ma Xingkong
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Can anyone suggest a mathematical model for predicting future values?

I would like to know, a mathematical model, which suits in predicting future values at different time based on past values . In my problem, a list nodes have different speeds at different time; I want to estimate speed of all nodes in future using…
Prasanna venkatesan T
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How to find the probability function and distribution function of Y=|X-3|

If the random variable $X$ has probability function x 0 1 2 3 4 5 p(x) 0.03 0.06 0.13 0.20 0.31 0.27 ,specify the probability function, distribution function, mean and variance of…
user507124
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