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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Probability Density function vs Mass function

I am a bit confused by using Probability Mass Function and Probability Density Function. I understand that for discrete case like Bernoulli or Binomial, we call it pmf. For continuous case like normal distribution we call it pdf. I have encounter…
K_R
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$L^2(\mu)$ limit of a sequence of CDFs

Let $(F_n)$ be a sequence of cumulative distribution functions (CDFs*). Let $\mu$ be a finite measure on $(\mathbb{R}, \mathcal{B})$, and assume $\mu$ is equivalent to Lebesgue measure (notice that any CDF lies in $L^2(\mu)$). Assume $\Vert F_n -…
user127022
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Joint Probability Density function: How to bound limits of integral

The joint density of Y1 , the proportion of the capacity of the tank that is stocked at the beginning of the week, and Y2 , the proportion of the capacity sold during the week, is given by f(y1,y2)={ 3*y1, if 0 ≤ y2 ≤ y1 ≤ 1, 0,…
CapturedTree
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Gamma distribution as the sum of exponential random variables

Let $X_1, X_2, \ldots X_k$ be i.i.d r.v.s from the exponential distribution. Let their pdf be: $f(s) = \lambda e^{-\lambda s}$. The pdf of the gamma distribution can be got by considering the $k-$convolution product of these pdfs. However, when I…
sntx
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Cumulative Distribution Function with Infinite Series

A discrete random variable $U$ follows a geometric distribution with $p = \frac{1}{4}$. Find $F(u)$, the cumulative distribution question of $U$, for $u = 1, 2, 3 ...$ $$F(u)=P(U
StopReadingThisUsername
  • 1,553
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Distribution of sum of two random variables.

We are given two Independent Identically Distributed random variables $X$ and $Y$ where $X,Y$~$U(0,1)$. Letting $Z=X+Y$ , we need to find the distribution of $Z$. The text I am reading goes as follows : $f_Z(z)=\int_{-…
User9523
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Find the probability that X lies within one standard deviation of the mean.

The random variable X has a Poisson distribution with mean $μ=5.55$. Find the probability that X lies within one standard deviation of the mean. Using my calculator, I found $P(3.19
StopReadingThisUsername
  • 1,553
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$f(x)=\frac{k x^3}{(1+2x)^6}$ if $x \in D=(0,\infty)$. Find distribution of $Y=\frac{2X}{1+2X}$.

Suppose the probability density function of $X$ is given by $f(x)=\frac{k x^3}{(1+2x)^6}$ if $x \in D=(0,\infty)$. Let $Y=u(X)=\frac{2X}{1+2X}$. Then $u(D)=(0,1)$. Since $u(x)$ is increasing on $D$, $u(x)$ is one-to-one on $D$ and has an inverse…
Shafat Arbaz Alam
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Finding the Cumulative Probability Distribution?

Given $f(x,k) = 2$ for $0 \leq k \leq x \leq 1$. Find The cumulative probability distribution $$ F(k_0) = P(K\leq k_0) $$ The hint is you must integrate at the joint. Does anyone know how to do this problem? I think you need to use a double…
Drew Smithe
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Finding the conditional distribution.

A penny and dime are tossed. Let $X$ denotes the number of heads up. Then the penny is tossed again. Let $Y$ denotes the number of heads up on the dime(from the first toss) and the penny from the second one. We need to find the conditional…
User9523
  • 2,094
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Iterating an experiment with bounded non-constant probability of success

Assume that we have an experiment $A$ which has the outcome "success" or "failure". Each time we try $A$ the probability of getting a success is different but always less than or equal to a given constant $p~(0
Ioannis Kokkinis
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cumulative distribution function(cfd)

If $f(y)=3(1-2y+y^2)$ where $0
Alyah
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Probability density of a sum of exponentially distibuted variables

The $X_1, X_2, \dots\ X_n$ are identical independently distributed random variables. $X_i \sim \lambda e^{-\lambda x}$. Find pdf of their sum.
Dmitri K
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Normal distribution, find $k$ for which $P(20\le X\le k)=0.4641$

I am having a problem solving the following. Find $k$ such that $$P(20\le X\le k)=0.4641$$ where $X$ is the normal random variable, given mean 20 and variance 4. I tried finding the $z$ values but got stuck since I can't find a value for $k$. I…
amine
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derived pdf of a function of random variables that is a power law.

someone told me that the derived distribution of the following function of RVs is a power law distribution. The special thing is that such conclusion was said to me without having knowledge of the original pdfs of X and Y ...I believe such a…
Philip
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