# Tagged Questions

Questions on using, finding, or otherwise relating to probability distributions, pdfs, cdfs, or the like.

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### Bernouli Trial Probability of Stopping After X Trials

The probability of a trial being a success if 0.30 Trials are repeated until 6 are successful. I'm asked to find the probability that the trials are ended after the 7th. (The 6 successful trials ...
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### Find the $p_{Y|X}(y|x)$ without the jointly probability

Let the distribution $Y = X + N$. Where $X$ and $N$ are independents and they have distinct distributions. I have $f_X(x)$ but I don't have the $f_{XY}(x,y)$ to use, for example, the following ...
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### Determining the Expected value of a random variable

Suppose we have a Poisson process of parameter $\lambda$. Each event of this Poisson process represents a start date of a period which duration is a random variable that follows an exponential ...
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### Conservation of Kinetic Energy in Vlasov-Poisson System

I'm studying the very basics of kinetic theory in Vlasov Poisson Systems, and the first equation I'm studying is the free transport equation, i.e.: $$\frac{\partial f}{\partial t}+v\cdot\nabla_{x}f=0$$...
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### Show $\int_{-\infty}^{\infty}\,f(u,t)dG(u)$ is a ch.f. where $G$ is a d.f. ; $f(u,\cdot)$ is a ch.f. and $f(\cdot,t)$ is continuous.

Show $$\int_{-\infty}^{\infty}\,f(u,t)dG(u)$$ is a ch.f. where $G$ is a d.f. ; and $f(u,\cdot)$ is a ch.f. for each $u$ and $f(\cdot,t)$is continuous for each $t$. Note that ch.f. means "...
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### What is the probability that two univariate Gaussian random variables are equal?

Let $X_1$ and $X_2$ be two independent univariate Gaussian random variables, s.t. $$X_1\sim \mathcal N (m_1,\sigma_1^2)$$ $$X_2\sim \mathcal N (m_2,\sigma_2^2)$$ So now what is $P(X_1=X_2)$? I tried ...
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### Coutinuous distribution in Probability

If suppose there is an interval $[a,b]$ then choosing a number from it is equal probable and a number can be any real number within the interval. Is it a case of continuous distribution ? How to ...
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### Prove that $f(x)=exp(-x-e^{-x})$ for $x\in \mathbb{R}$ is a p.d.f and find the c.d.f.

Prove that $f(x)=exp(-x-e^{-x})$ for $x\in \mathbb{R}$ is a probability density function and find the cumulative density function. I think that by proving that $f(x)$ is a pdf, it should be fairly ...
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### Jar and Ball Probability Distribution

If I have 8 jars, each jar contains 5 unique ball types. However, I know that I have 20 unique ball types out there. So, I have balls labelled from B1, B2, B3, ...B20 to put into 5 jars. Let's say ...