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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Find the probability of $(X_1 < X_2)$

If I have $2$ independent random variables $X_{1}$ and $X_{2}$, how can I prove that $Pr (X_{1}
user 2000
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Obtaining the marginal distribution given the joint mass

Let the joint mass of $x$ and $y$ have the joint density as: $P(X=x,Y=y)=\frac{e^{-1}}{(y-x)!x!2^y}$ where $x=0,1,2,....,y$ and $y=0,1,2...$. It is required to obtain the marginal distribution of both the random variables. My approach I obtained…
userNoOne
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Biased coin probability when p can lie in a range of values

I can't find anything like this problem online, any help would be greatly appreciated. This isn't homework, just a thought experiment I can't solve. You are testing a new coin that is designed to land on heads greater than 70% of the time. How many…
user3341881
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Probability joint distribution on probability mass function

Two dice are tossed. Let X be the smaller number of points. Let Y be the larger number of points. If both dice show the same number, say, z points, then X = Y = z. (a) Find the joint probability mass function of (X, Y ). (b) Are X and Y independent?…
Satyaki Chatterjee
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Product of a exponential and discrete Distribution

Let $U \sim e(1)$ and $V$ a discrete random variable independent of $U$ such that $p_V(v)=1/2$ if $v \in \{-1,1\}$ and $p_V(v)=0$ otherwise. Problem: Let $W=UV$. Find the distribution function of $W$ $\forall w\in \mathbb{R}$. My…
Mathe
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Probability Distribution of Blood Sample Test

I have been trying to find out below problem; Suppose 10 patients are to be tested for a blood disease and that the test in guaranteed to detect the disease. Furthermore, suppose that the probability that a patient has the disease is 0.02 and that…
Kamuran Karam
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Mean and variance of distance to a point on a circle

If $P$ is a random point on the circle $x^2+y^2=1$, what are the mean and variance $P$'s distance to $(0,1)$? The random variable has the function $$X=\sqrt{-2x+2}$$ can't quite figure out what to do next...
pi47
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What exactly is meant by "the distribution of a random variable"?

So I've started statistical distributions this week, and there's one piece of terminology that throws me, and this is the idea of a distribution. I understand for most people (on this site, at least) this term is common knowledge, but as someone who…
joshuaheckroodt
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PDF of a function with two noise sources

I have the following function: $$h(t)=L(t)\dfrac{EFL}{d_0-v(t)t}$$ $EFL$ and $d_0$ are know constants. $L(t)=L_0+\nu(t)$ and $v(t)=v0+w(t)$ where $L_0$ and $v_0$ are constant. $\nu(t)$ and $w(t)$ are random variables normally distribuited.…
Riccardo.Alestra
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How to understand Variational Autoencoder

As new to variational autoencoder, there are some simple details perplex me. The basic idea of VAE is to use an encoder to map some unknown distribution (e.g. mnist images) to a specific distribution like Gaussian, and then decode this latent…
Jermmy
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Elliptic Distributions vs Rotationally Invariant Distributions

I'm trying to understand the difference between Elliptic and Rotationally invariant distributions. Previously, for some reason, I was under the impression that the Gaussian distribution was the only rotationally invariant distribution, i.e. it is…
Student
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Finding the Expected value and Variance of the Binomial probability distribution

Let $X \sim \text{Binomial}(n,p)$, that is, the probability mass function of $X$, $f(x)$, is such that $$f(x) = \begin{cases} {n \choose x} p^x (1-p)^{n-x} & \text{for } x=0,1,2,\ldots,n\\ 0 & \text{otherwise} \\ \end{cases}$$ I have to find…
animorphlover3
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Prove that $P(X \le n)-P(X+Y \le n)= \alpha P(X+Y=n)$

Let $X$ and $Y$ be mutually independent random variables taking non-negative integer values. Prove that $P(X \le n)-P(X+Y \le n)= \alpha P(X+Y=n)$ holds for $n=0,1,2,...$ and for some $\alpha>0$ iff $P[Y=n]=\frac{1}{1+ \alpha}(\frac{\alpha}{1+…
user321656
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joint pdf of two random variables

A pair of random variable $(X, Y)$ is uniformly distributed in the quadrilateral region with $(0,0),(a,0),(a,b),(2a,b)$, where $a,b$ are positive real numbers. What is the joint pdf $f(X,Y.)$ Find the marginal probability density functions $f_X…
Deepsea234
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What is the PDF of the sum of N drawings from a PDF

Suppose we have a random variable $X$ with probability density function $f(X)$. Let $Y$ be the sum of $N$ draws of $X$. What is the PDF of $Y$?
Lars Ericson
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