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 min

I have random values $X,Y$ and $f(x,y) = 2x+4y$ , where $0\le x\le 1$ , $0 \le y \le 1-x$ How to calculate distribution of $Z = \min(X,Y)$ ? As I calculated, $X$ and $Y$ are dependent, because $f(x) \cdot f(y) \neq f(x,y)$
Armyx
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When f is a probability density function

How to determine $C$ if $f$ is a probability density function? $$f(x,t)=\dfrac {1}{C\sqrt{t}}e^{-\dfrac{{x}^2}{4t}}$$ Should I integrate the integral $$\int_{-\infty}^{\infty}f(x,t) \ \ dx$$
pimbi
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Probability distribution functions

If the probability density function is ($0\le x \le 1, 0\le y \le1$): (i) $f_{X}(x) = \frac{3x^{2}}{2} + x$ (ii) $f_{Y}(y) = \frac{3y^{2}}{2} + y$ Find the distribution functions $F_{X}(x) = P(X\le x)$ and $F_{Y}(y) = P(Y\le y)$. Can someone check…
user2850514
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Calculate the Cumulative density.

$U$ is a random variable in the range of $(0,3)$. The random variable $W$ is the output of the clipper described by $W=g(U)=U$ for $U\le 1$ and $1$ for $U>1$ find the cdf of $FW(w)$ Any ideas on how to solve this? My idea was to graph it $g(U)$ vs…
SeahawksRdaBest
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estimating probability of a point sampled from a distribution

Assume we have a d-dimensional vector space.Also, we don't have a parametric distribution function, only we have a set of samples in this space which we assume is sampled from one unknown distribution ,what is the best way to compute the probability…
user85361
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Strict Inequality Using CDF

Considering the definition of cumulative distribution function: $$F_{x}(x)=P[X\le x]=\int_{- \infty}^{x} f_{x}(x)dx$$ where $f_{x}$ is the probability density function of $x$, how can one obtain $P[X< x]$ ? (Note the strict inequality)
user147813
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conditional on X=x Y is binomial(X,p), What is E(exp(y)/X=x)

Suppose we know conditional on X=x Y is binomial(x,p) where p is known.What is E(exp(y)/X=x) where exp is the expodential function and E the expectation Any help will be appreciated Thank, You
TheGeometer
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Normal Distribution, probability that X differs from expected value by less than 10%

I have a normal approximation of binomial, $X\sim \mathcal{N}(36,4.6475)$. I have to find the probability that the number of red blocks ($\mu = 36$) differs from its expected value by less than $10\%$. I know how to calculate normal distribution, I…
Deo
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Moments of a probability distribution

$X_{1} \sim B(n_{1},p_{1})$ and $X_{2} \sim B(n_{2},p_{2})$ are independent. Let $Y = X_{1} + X_{2}$. I have worked out the moment generating function to be $$M_{Y}(t) = (p_{1}e^{t} + 1 - p_{1})^{n_{1}}(p_{2}e^{t}+1-p_{2})^{n_{2}}$$ Now to find the…
user2850514
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T-Intervals and % Confidence Interval

The question is the following: " A random sample of six 2009 sports cars is taken and their "in the city" miles per gallon is recorded. The results are as follows: 23 19 24 17 16 22. Assuming the population distribution is normal, calculate the 99%…
Alexa
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Pivotal quantity of Weibull distribution

If I have $X_{1},\ldots,X_{n}$ a random sample from a Weibull distribution $X\sim WEI(\theta,2)$.How can I show that $Q=2\sum\limits_{i=1}^n X_{i}^2/\theta^2\sim \chi^2(2n)$. I have not learnt any transformations for Weibull distributions. I believe…
Lotte
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Galton Machine and Unpredictability

We are all familiar with the Galton Machine and the images of the balls cascading through the device and ending up in bins which ultimately show a likeness to the binomial distribution. Most everyone will agree that the balls exhibit random and…
william hird
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Sum of distribution

If $X_i \sim Bernoulli(\theta)$, then the $\sum_1^n X_i \sim Binomial(n, \theta)$ I don't know how it is derived, could anyone show or prove it to me. Besides, there are similar knowledges such as $X_i \sim Exp(1/\theta)$, then the $\sum_1^n X_i…
user137354
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Distribution of the product of Gaussian column matrix and Signed Bernoulli matrix

This is not a homework question though it might be trivial for those who are well versed with multivariate distributions. I am trying to understand a paper that has the following product form. Let $A$ be a row matrix that has only single entry…
Jalaj
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How to find the distribution of X from the moments of X?

For example the moments of X is defined by E(x^n)=0.7, for $n\in[1,\infty]$. How to get the distribution of X?
Bobai
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