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
1
vote
1 answer

What is the name of the random distribution whose samples have a scale that is uniformly random scale within a given range?

In Machine Learning, during hyperparameter tuning, if you don't have a clue about the scale of the hyperparameter that you are trying to tune, it is common practice to perform grid search with roughly geometrically increasing values, for example:…
MiniQuark
  • 155
1
vote
0 answers

reference on some hitting time

I am looking for references about some probability distribution. Here are some elements of definition. Associated probabilities Support : $T(\Omega) = \mathbb{N} \backslash \{0,1\}$ Probability mass function : $\forall k \in \mathbb{N}^*, P(T = k)…
marsupilam
  • 111
1
vote
1 answer

What is the density of the quotient of two independent standard uniform random variables?

$X$ and $Y$ are independent standard uniform random variables. What is the density of $Z = X/Y$? So far I have: $$f_X(x) = f_Y(y) = 1\text{ if }0 \le x,y \le 1$$ $$\begin{align} f_Z(z) & = \int_{-\infty}^\infty f_X(zx)f_Y(x)|x| dx \\ & =…
woaini
  • 335
  • 1
  • 5
  • 18
1
vote
0 answers

Given PDF of X, find CDF of Y, where Y = X^2

I'm given a PDF of X, such as $f_x(x) = \frac 12 \lvert x \lvert$ for $-2 \le x \le 2$, and $ 0 $ otherwise, and told to find the CDF for Y where $Y = X^2 $. Trying to do this problem, and others like it, there's two places that trip me up every…
Yuerno
  • 167
1
vote
1 answer

How to recognize what type of probability distribution to use in solving probability problems?

We have: Bernoulli's, Binomial, Geometric, Hypergeometric, Negative binomial, Poisson's, Uniform, Exponential, Normal, Gamma, Beta, Chi square, Student's distribution. I would like to know how and when to use each of these distributions when solving…
user300047
  • 179
1
vote
0 answers

Bimodality of a probability density function

I have a probability density function $f(x)$ that is based on two parameters $p$,$q$. Using mixing rule, I created another density function $$g(x) = C\cdot F(x) + (1-C)\cdot G(x) $$ where $F(x)$ is $f(x)$ using $p_1,q_1$ as parameters and $G(x)$ is…
user424072
  • 21
1
vote
1 answer

Why $e^{\frac{-130}{100}}$ for p?

I am trying to understand a solution to a problem. Here's the problem. Abe will sell his calculator to the person to offer him at least \$130 for it. The offers are independent exponential random variables with mean $100. What's the expected number…
John Hoffman
  • 2,734
1
vote
1 answer

If $X\sim\mathcal{N}(\mu,\sigma)$, what's the CDF of $X u(X)$?

Let $X \sim \mathcal{N}(\mu, \sigma^2)$ be a gaussian random variable. What is the CDF (Cumulative Distribution Function) and (if it exists) the PDF (Probability Density Function) of the variable $$ Y = X u(X) $$ where $u(\cdot)$ is the unit step…
PseudoRandom
  • 1,344
1
vote
1 answer

How to sample empirical probability density function

I'm looking to sample a probability distribution function (let's call it $F$) where the frequencies of the different (discrete) events are collected empirically. Since it is collected empirically, I do not have a closed-form expression for $F$. If…
index
  • 385
1
vote
1 answer

Uniform joint PDF's

Let $X$ and $Y$ be two random variables. Their joint PDF is uniform in the region $0$ to $1$ (inclusive). Let $Z$ be a random variable defined as $Z = \min\{X,Y\}$. Determine $f_Z (z)$, $f_{Z\mid X}(z\mid x)$, $E[Z],$ and $E[X\mid Z=z] $ I'm…
Hoser
  • 335
1
vote
1 answer

Find a constant in a density function

$ f(x) = \begin{cases} k\sqrt{x}, 0
Justin H.
  • 13
  • 1
  • 4
1
vote
1 answer

Plotting a Joint Probability Density function

I have a problem where I have two independent variables each having a probability density function given by: $p(s_1) = \frac{1}{2}\sqrt{3}$, when $s_1\leq\sqrt{3}$ and $0$, otherwise And the probability density function is the same for other…
shaunshd
  • 95
1
vote
1 answer

Chebyshev Theorem

From a lot of 10 missiles, 4 are selected at random and fired. If the lot contains 3 defective missiles that will not fire, what is the probability that (i) all 4 will fire, (ii) at most 2 will not fire? Finally, use Chebyshev theorem to interpret…
as2d3
  • 125
1
vote
2 answers

weighted empirical cdf consistency/unbiasedness?

The weighted empirical distribution function estimator is given by: $\hat{F}(x)=\frac{1}{\sum_{i=1}^{n}w_{i}}\sum_{i=1}^{n}w_{i}I(X_{i}\leq x)$ see also here: http://www.okstate.edu/sas/v8/sashtml/insight/chap38/sect25.htm I fail to find…
leo
  • 286
1
vote
1 answer

Minimum between gamma and exp

For $X_1,X_2 \sim Exp(\gamma_i)$ it is known that $ Min\{X_1,X_2\} \sim Exp(\gamma_1 + \gamma_2) $ and $ \Pr(X_1 < X_2) = \dfrac{\gamma_1}{\gamma_1+\gamma_2} $ Can we say something similar when one of the variables is distributed gamma? For $X…
Cohensius
  • 301
1 2 3
…
99 100