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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How to derive Probability Distribution of this r.v?

$y$ is a random variable \begin{equation} y=ax+n \end{equation} where $a$ is a scalar, $x \in \{ +1,-1 \}$ and $n \sim \mathcal{N}(0,\sigma_c^2)$. We define \begin{equation} L(x)\triangleq \ln \left( \dfrac{Prob(x_i=+1) }{ Prob(x_i=-1)}…
NAASI
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Spliced probability distribution modeling

I have a simulation model for insurance claims that works as follows: Assume random values come from two distributions defined as $$ \begin{eqnarray} f_1(x)&, & 0 < x \leq c \\ f_2(x)&, &x > c \end{eqnarray} $$ A random value will fall in…
MrActuary
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Coin flipping combined with exponential distribution

Let $Z\sim \exp(1)$. Let $X$ be a new random variable (rv) defined as follows: We flip a coin. If we get head, than $X=Z$, and if we get tail than $X=-Z$. I'm trying to figure whether $X$ is a discrete, continuous or mixed type rv, and to calculate…
Brassican
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Probability - Limits of integration for Z=X+Y, with bivariate density f(x,y)

It is given that $$f(x,y)=\begin{cases} 864(2x-y)(y-x), & x \le y\le 2x, x+y \le 1\\ 0, & \text{otherwise} \end{cases}$$ Find the density $f_z(z)$ for $Z=X+Y$ I have used the formula for convolution that says…
Wstate123
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Binomial distribution Question about the product of two individual random variables

How do you solve this question: Consider two independent binomially-distributed random variables $X \sim B(2, a)$ and $Y \sim B(2, b)$. Let $W$ be the random variable that represents the product of each value of $X$ with each value of $Y$. Construct…
Maths2468
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Why the equation can be equal to $(1-p)^k$?

I was studying for geometric random variable, and I saw that $$P(X>k)\sum_{i\ge k+1}p(1-p)^{i-1}$ =$(1-p)^k$$ I don't understand why it can be equal to $(1-p)^k$?
user277100
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Expectation of Y in a joint distribution?

Let $X$ be a uniformly chosen number in the interval $(0, 1)$. Choose a point P uniformly from the triangle with vertices at $(X,0), (0,X)$, and $(0,0)$. Let $Y$ be the $y$ coordinate of the point P . Compute $E(Y )$. Here is my work: Here is what…
user3904534
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If $X$ has an exponential distribution, prove the hazard function is constant

$X$ has an exponential distribution, $Pr(X>0)=1$, p.d.f is $f$, c.d.f is $F$. $h(x)=\frac{f(x)}{1-F(x)}$ for $x>0$. Prove that $h(x)$ is constant for $x>0$.
perry zhu
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joint distribution and order of variable

I was reading a lecture regarding representing a join distribution as a graphical model. The lecture is available here (on page 4 of the slides): http://www.maths.lth.se/matematiklth/personal/sminchis/mlc/lecture-6.pdf In the lecture, it…
john_w
  • 580
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modelling using Binomial p.d.f

I am trying to get expected number of days for one to get a loss of more than 5 Yuan, if it costs 2 Yuan to use a coffee vendor machine that has a success rate of 99% per vending. I try the machine twice per day. What is the probability of success…
user291529
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Monotone likelihood, symmetry and monotonic densities

Suppose, there are two distributions over [0, 1] such that $F(x)=1-G(1-x)$ for all $x\in[0,1]$ and monotone likelihood ratio holds, i.e. $\frac{f(x)}{g(x)}$ is increasing in $x$. Does that necessarily imply that both $f(x)$ and $g(x)$ are monotonic?…
fencer
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Does this random variable built from log normals have a recognizable distribution?

Let $X_t$ be a standard Brownian motion, and $\lambda$ and $\alpha$ are positive constants. Consider the random variable: $$ \int_0^t \lambda e^{\lambda u + \frac{\alpha u X_t}{t} - \frac{\alpha^2 u^2}{2t}} du$$ Does this guy have a standard…
quasi
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What type of probability distribution is this?

This is probably a simple question, but I would like to check what kind of distribution is this? Is there a name for such distributions? $\Pr(X=k)=0.4−0.1k$, $k=0,1,2,3$
Kexis Reeves
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Relation between two independent Poisson process

Consider two independent Poisson process A, B which have rates $\lambda_A$ and $\lambda_B$. The question is to find the distribution of difference of time between event B and the last event A before it. At first sight I thought that since we can…
Rick Pan
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Finding standard deviation of a normal distribution curve.

I've been working on this problem and I just can't seem to come up with the right answer. The question goes: Consider a normal distribution curve where 60-th percentile is at 11 and the 25-th percentile is at 9. Use this information to find the…
Cheul Hee Jason Yoo
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