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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Distribution of A=1/B, where B is normally distributed.

Take a variable, B, which has standard normal distribution. Let A = 1/B. What is the distribution of A? One way to go about this problem would be to take the CDF of the standard normal curve, and to use this to compute points on the new…
Thomas Delaney
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For which pair of probability density functions, $L=f_1(x)/f_0(x)$ is increasing?

One addition to the title: For $(\Omega,\cal{F},P)$, $\Omega=\mathbb{R}$. Thanks in advance. I hope there are some others than only Gaussian (with same variance!).
Seyhmus Güngören
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How may I generate a distribution which follows power law?

I would like to generate a distribution which follows a power law in a rather peculiar way. I have a lot of marbles, I take one of them at a time and put in a set with a certain distribution of probability: let's say that when I take marble N there…
mau
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Continuous probability distribution

I dont understand how for a continuous probability distribution f(x) that the probability of getting one individual x is 0. Surely if you put a value into your formula this gives the value of the probability of that one value ?
Mr. Electron
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Can Months be used in a Discrete Probability Distribution?

this concerns one of my projects in Statistics. I am going to measure the frequency of my classmates' birthmonths and going to provide a probability distribution along with it. I am just wondering if it is even possible?
JB-0002
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What are important distributions to be familiar with?

I'm wondering what are some important distributions to know the basic properties of (pmf/pdf, mean, variance) specifically as it comes to times series analysis, financial analysis, and machine learning. I've gone through the basic ones (Bernoulli,…
jhlu87
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at least 1 remainder has a 1 at the 2nd decimal place

Let X be >= USD 10.00 to <= USD 49.99 We distribute to 10 person unevenly with an random amount. What value is X which will yield at least 1 person amount that ends with USD x.x1. that is the last decimal digit of the cents is 1 ?
miko mah
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Probability Distributions of 2 variables

Consider two continuous random variables X and Y with joint p.d.f. $f_{X,Y}(x,y) = \frac{x+2y}{24}, 0
S.Kumar
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Something about the beta distribution?

I am trying to understand $\beta$-distribution, but could not understand how to select the values of $\alpha$ and $\beta$. To my understanding, the higher the value of alpha, it means more success probability. Another issue is what does the value of…
SJa
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Why is it possible to have $Y \sim Binomial(100, 0.5)$ with $P(X \ge Y) = 1$

Let $X \sim Binomial(100, 0.9)$. Apparently, it is possible to have another random variable $Y\sim Binomial(100, 0.5)$ for which $P(X \ge Y) = 1$. How is that possible? I don't feel that it is because $0.5 < 0.9$.
Minden Petrofsky
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Distribution of sum of two dependent variable

X conforms to a normal distribution with mean a and variance b. Every time I randomly generates a value of X first, say x0. If x0 is greater than preset threshold Q, then I generates Y from another normal distribution with mean c and variance d. If…
Lovnlust
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Probability problem choose 400.000 from 1.000.000

When i have 1.000.000 different numbers from 1 to 1.000.000 and 400.000 people choose one of them how can i calculate the probability to choose for example 300.000 or 200.000 or x DIFFERENT numbers? In other words how can i calculate the…
Damian
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How to calculate the Probability of Lead Size X occurring at some point in a Coin Tossing Game of n Tosses?

After watching the biggest lead in Superbowl History evaporate, I looked for info in Feller's classic chapter on coin toss leads, but could not find anything about how to calculate the expected distribution of Lead Sizes at any point during a Coin…
Pseudoego
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Distribution of difference between Gamma(2,1) and Exp(1)

As the first answer in a link shown , $T\sim {\rm Gamma}(2,1), S\sim {\rm Exp}(1)$, we have two properties: $T-S\sim {\rm Exp}(1)$, $T-S$ is independent of $S$. I cant prove them. Esperically for Question 1, I find that, $Z = T-S$, ${\rm…
William_Third
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What is the value of A for this F(x) distribution to be valid?

Let $$F(x) = A(1 - \dfrac{1}{e^{x-1}})$$ where $1 < x < \infty$ and $0 \leq F(x) \leq 1$ The question is asking to solve for $A$. My idea is that, $$y = (1 - \dfrac{1}{e^{x-1}}) \in (0, 1)$$ which implies $$0 \leq Ay \leq 1$$ Thus $0 \leq A \leq…
roxrook
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