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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basic moment generating function

I came across a piecewise function which seems pretty basic, but I don't know how to find the moment-generating function. If $X$ has the pdf $f_X(x)=x$ for $0\leq x\leq 1$, $2-x$ for $1\leq x \leq 2$ and $0$ elsewhere, how do we find $M_X(t)$?
johnnymath
  • 877
2
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Normalized sum of uniformly distributed random variables

Let $X_1,\dots,X_n \sim U([0,1])$ be $n$ i.i.d. random variables uniformly distributed over $[0,1]$. Define for all $i = 1,\dots,n$, $Y_i = X_i/\sum_{i = 1}^n X_i$. Does this correspond to some well-known family of distributions? What is the…
Spark
  • 399
2
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finding two Zipf distributions out of one Zipf distribution

$\newcommand{\pop}{\operatorname{pop}}$Assuming $ G = \{g_1, g_2, g_3, \ldots , g_{N_G}\}$ is set of all the globally existing data objects. The total request rate for $G$ is shown by $\lambda_G$. The popularity of data objects in $G$ follows a Zipf…
Alireza Montazeri Gh
  • 107
2
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1 answer

Compound of two exponential distributions

What is the distribution of a exponential distribution, whose expected values is drawn from the expontial distribution $$X\sim\mathrm{Exp}(\text{mean}=\alpha) f(x\mid α) = (1/α) \exp(-x/α) $$ $$Y\sim\mathrm{Exp}(\text{mean}=X) f(y\mid x) = (1/x)…
Dan Munsone
  • 21
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convolution of two probability density functions

Please no one call me dumb - I am not a mathematician and haven't done proper math for the last ten years. But I have a problem at work where I need to perform a convolution of two probability density functions and I have no idea where to start.…
Linda
  • 21
2
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1 answer

Calculate the maximum probability of a result of rolling n dice of varying number of faces

Disclaimer: I'm a computer programmer more than a mathematician, so reading text like that of the answer to this question is a little (read: a lot) over my head. I've written an algorithm (brute-force, O(nk) running time, where n is the number of…
dx_over_dt
  • 143
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Probability of being between two independent Gaussian random variables

Suppose we have two independent random variables $X$ and $Y$. I am interested in calculating $P(X\leq x \leq Y)$. Is this correct? $$P(X\leq x \leq Y) = P(X\leq x)P(Y \geq x) = P(X\leq x)[1 - P(Y \leq x)]$$ If X and Y are Gaussian random variables,…
Jeremy
  • 31
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combined random variables and pdf

I need some advice to how I would begin my integration for the following problem (as in, I do not understand the region of integration): If we have a joint pdf, say $f(x,y)=4e^{-2x-2y}$ for $x,y>0$ and $A=\min(X,Y)$, how do we find $P(A>a)$ for…
johnnymath
  • 877
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Permutation and combinations (Sheldon M.Ross)

We need to divide 8 new teachers among 4 schools , how many such divisions are possible ? I tried to solve this by the Distribution Method , that is : $x_1$ + $x_2$ + $x_3$ + $x_4$ = 8 , which gives the solution as ${11 \choose 3}$ , is this…
User9523
  • 2,094
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1 answer

When Benford´s Law doesn´t apply - p(d) = (10.5 - d)/(49.5) instead

When Benford´s Law doesn´t apply I would like someone validate (or not) the formula (A) Suppose I pick some book and open it at random. What the probability for first digit page being 1 ? Related problem: walking on street with blinded eyes, what…
Miguel Velilla
  • 309
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2 answers

What is the appropriate probability distribution to model this situation?

I want to model a random variable which represents the number of failures before success in a repeated Bernoulli trial. I will conduct only utmost N trails and I am guaranteed of one success (only one success possible) if N trials are conducted.…
suresh
  • 165
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How to draw marginal density function using R?

suppose $f(x,y) = cxy^2$ is the joint pdf of $X$ and $Y$. $0\le x\ ,\ y\le 2$. Q1: what value must $c$ have for this to be a pdf? Q2: what is the marginal distributions of $X$ and $Y$. Q3: draw a graph of each marginal density function using…
Yilin Wang
  • 307
2
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1 answer

Cumulative distribution of first success in bernoulli trials with p = 0.5

A box contains a very large number of balls, so that the probability of choosing a white or red (initially at equal numbers) remains at 1/2 as balls are chosen. Let X be the number of balls chosen at random until a red ball is chosen. Determine the…
Laweng
  • 21
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1 answer

Find the distribution of the min(X,Y) where X and Y are independent and exponentially distributed.

Find the distribution of U=min(X,Y) where X and Y are independent random variables and both exponentially distributed with parameters lambda and mu respectively. The only headway I have made is that P(U< u)= P(X< u)P(Y< u) by considering the joint…
guest10923
  • 59
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1 answer

Distribution for this Probability density function?

I having problem recognizing the following distribution. The random variable has density $$f_\theta(x)=\frac{x}{\theta}\exp(-x^2/ 2\theta)1_{(0,\infty)}(x)$$ with respect to lebesgue, with parameter $\theta>0$. Edit: A few more questions :D When we…
ChuckP
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