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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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Poisson distribution for rare event

I was taught in school that Poisson distribution is usually used to model rare events. And I understand the Poisson process is such that the probability of an event in one interval is independent of another interval and the probability depends on…
user3119750
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equate normal CDFs of different parameters

I am looking for a closed form relation between $x_1$ and $x_2$ that equates two normal CDFs of the same mean but different standard deviation: $F(x_1;\mu,\sigma_1)=F(x_2;\mu,\sigma_2)$ Also, as a follow up I am looking for a similar relation…
Sam
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Probability: Transform to a arbitrary probability distribution

I need help with this one this is a exercise in when I need to show all the step
Sophi
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What is pdf of Negative Binomial distribution

Exactly what is the definition of pdf of negative binomial distribution? So I have two textbooks one said: $$f_X(x)=\begin{pmatrix} r+x-1\\ x \end{pmatrix}p^rq^x$$ where as on the other it is defined as $$f_X(x)=\begin{pmatrix} r+x-1\\…
ttothef
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product of cumulative distribution function

For all integer $N>1$, I am trying to show that for a gaussian (or even better any type) cumulative distribution function $F(\theta;\mu,\sigma)$ ($\mu$ and $\sigma$ are the mean and standard deviation):…
Sam
  • 48
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Probability Strategy

A charity fund-raiser has found that active soliciting gains \$5 contributions with probability .7 and passive soliciting gains \$10 contributions with probability .4. No other contributions are made. What strategy should be pursued to gain the…
UserX
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Probability Distribution Function for Nonlinear Function

I have the following problem: Let the random variables X and Y have the probability density function (pdf) $$f(x, y) = \begin{cases} 1 & \text{for } 0
user130398
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finding a cummulative distribution function from a uniform density function

how can I find a cummulative distribution function from a piecewise uniform density function?
Clement
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Ball and Urn Problem, drawing equal number of blue and red balls.

An urn contains b blue balls and r red balls, b + r total. Balls are withdrawn one at a time without replacement. What is the probability that at some stage the number of blue and red balls are equal. I've gotten this far: Either b >= r or r >= b,…
lumcti
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mixture of multivariate Gaussians is elliptical?

Let $\mathbb{R}^N$ be the ambient space and let $D_1$ and $D_2$ be different multivariate Gaussian distributions with the same mean (assume they are independent). Suppose further that $D_1$ is restricted to a proper subspace (for simplicity we can…
user21725
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Distribution of results of a biased coin

the mass distribution of a coin is so that the chance of getting a head s only 40% .The coin is tossed a 100 times what is the chance -to get more than (inclusive ) 50 heads ? -to get more than (exclusive) 50 tails? to get more than (exclusive) 60…
user16457
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Gaussian distribution with gaussian parameters

Let $X \sim \mathcal{N}(M, S)$, where $M,S$ are themselves gaussian random variable with mean $\mu_{M,S}$ and variance $\sigma_{M,S}$. Does this distribution have a particular name/form? Can we compute its CDF?
jojo87
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Proving the equivalence of a pdf with a log-normal distribution

I have the following function normalised to 1 on $(0, \infty)$: $$ g(x) = \frac{e^{-\left(\mu + \frac{\sigma^2}{2}\right)} e^{-\frac{(\mu -\text{Log}[x])^2}{2 \sigma ^2}}}{\sigma \sqrt{2 \pi }} $$ which, after multiplying by…
mattek
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Poisson distribution question, reading from the table

The number of cars passing over a certain bridge between 11pm and midnight has a Poisson density with lambda = 4. In what proportion of nights would you expect more than one car to pass over the bridge during this time? I've already worked out,…
Arvin
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Distribution of the degree of a node in a random graph in the unit circle

My question is about the degree distribution of a special random graph. Suppose $n$ points are uniformly and independently chosen in a unit circle. Join two points iff they are within a distance of $r$, where $0
AgnostMystic
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