# Tagged Questions

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

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### How do I find the marginal distribution with this summation/series?

Let $X$ be a Poisson(2) and $Y$ be Binomial(10,3/4) random variables, If $X$ and $Y$ are independent, then $P(XY=0)$ is I thought of using transformation to find the distribution of $XY$ so I let ...
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### Finding the conditional distribution of 2 dependent normal random variables

Here's the situation $X \sim N(\mu, \sigma^2)$ and given $X=x$, $Y \sim N(x, \tau^2)$ I need to find the distribution of $X$ given $Y=y$ From what's given, I know the pdf's of $X$ as well as ...
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### Deriving Time of extintion of a Small neural Network

I'm trying to derive the Expected Value of the Time of Extintion $\tau_{ext}$ of a small Neural Stochastic Network with the following dynamics, where I consider $\tau_{ext}$ to be the time of the last ...
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### Distribution of a random variable waiting for a consecutive sequence of bits?

Suppose we're trying to transmit a message comprised of $n$ bits. Assume each bit has a probability $p$ of being correct. Success means we succeed at consecutively transmitting all $n$ bits. As soon ...
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### How to pick the same color spheres out of two boxes

For the following problem: There are two boxes $A$ and $B$. Box $A$ contains $3$ red, $8$ white and $13$ green spheres, while box $B$ contains $5$ red, $7$ white and $6$ green spheres. If we pick ...
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### fidi of Chi-square Random Field

The $\chi^2$ random field $U(t)$ with $n$ degree of freedom (dof) is defined as: \begin{align} U(t) = \sum_{i=1}^n X_i(t)^2, t\in\mathbb{R}^N \end{align} where $X_1(t),...,X_n(t)$ are i.i.d ...
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### Probability that a random variable is zero as expressed as limit of a sequence

Consider a random variable $U:\Omega \rightarrow \mathbb{R}$ defined on the probability space $(\Omega, \mathcal{F}, \mathbb{P})$. Suppose $U(\omega) \geq 0$ $\forall \omega \in \Omega$. Consider a ...
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### convergence in distribution of truncated gaussian variables

Let $X$ be a random variable which is distributed normally with mean $\mu=0$ and variance $\sigma=1$. Suppose that $X_n$ is a random variable for any positive integer $n$ with truncated normal ...
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### Finding marginal distribution, unit sphere

I'm asked to find the marginal distribution of $(X,Y)$ as $(X,Y,Z)$ is a point chosen uniformly on the unit sphere. I've worked out that the joint density function $f_{XYZ}(x,y,z) = \frac{3}{4\pi}$ ...
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### The distribution of the x-coordinate on unit circle

I'm trying to determine the distribution of the x-coordinate (uniformly distributed) on the unit circle (density function). I've seen some threads on this, such as this, where they use the method of ...