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
0
votes
1 answer

Multivariant marginal distribution

The marginal distribution of a individual RV of two discrete random variables $X$ and $Y$ is $$pX(x) = \sum_y pXY(x,y) $$ And if you have 3 disrete RVs $X$, $Y$, $Z$ is this correct? $$pXY(x,y) = \sum_z pXYZ(x,y,z) $$ And why so?
zahrim
  • 1
0
votes
1 answer

Tail of binomial Distribution (Confused)

If $X$ is the number of successes in a Binomial Distribution Then, $P(X \leq K) = \dbinom{n}{k} (1-p)^{(n-k)}$ However, when I apply it to the case where $p=0.003$ $n=1000$ $k=1$ I get $P= 50.43$!!! What am I missing??
user966168
  • 1
0
votes
0 answers

Need help finding $P(Z<0)$ with $Z=X-Y,\quad X\sim\mathcal{N}(0,1)$, and $Y\sim \Gamma(k,\theta)$

My probability theory is a little rusty so I'm having trouble finding a nice expression for $P(Z<0)$ where $Z=X-Y,\quad X\sim\mathcal{N}(0,1)$ is a RV with a standard normal distribution, and $Y\sim \Gamma(k,\theta)$ is a RV with a gamma…
I_AM_ERROR
  • 1
0
votes
1 answer

Calculate $P(|X-Y| \geq L/4)$ for two independent uniform random variable $X$ and $Y$

$X$ is a uniform random variable on [$0$, $L/2$] and Y is an uniform random variable on [$L/2$,$L$]. $X$ and $Y$ are independent. Calculate $P(|X-Y| \geq L/4)$. This is what I have so far. since $X$ and $Y$ are independent, the joint probability…
user59036
  • 1,525
0
votes
1 answer

Boundaries of the marginal density from a joint distribution

I know that to find the marginal density I need to compute $f(x) = \int_{-\infty}^{\infty}f(x,y)dy$ But when I have i.e. $f(x,y) = (1/θ^2)e^{-y/θ}$ for $0
ReRed
  • 277
0
votes
2 answers

If $X \sim HGeom(w, b, n)$, then $p = \dfrac{w}{w + b}$ remains fixed if $N = w + b \to \infty$

My notes say the following: Theorem If $X \sim HGeom(w, b, n)$ and $N = w + b \to \infty$ such that $p = \dfrac{w}{w + b}$ remains fixed, then the PMF of $X$ converges to the $Bin(n, p)$ PMF. $HGeom(\cdot)$ is the hypergeometric distribution. What…
The Pointer
  • 4,182
0
votes
1 answer

Probability that Amy the cyclist will complete her route within 30 days (or less)

Amy has $30$ days of paid holiday, on which she decided to go for a bike journey in France. She chose a safe route of $2300$ kilometers. Every morning Amy tosses a die, and if the outcome is $k$, where $k = \{1,2,3,4,5,6\}$, she cycles $20k$…
Reece
  • 45
0
votes
1 answer

Probability of the temperature lying in-between $281K$ and $291K$ for a certain distribution

Using the following PDF with values of: The following graph can be formed: The minimum and maximum values are: minimum = $243.483K$ maximum = $308.05K$ How can I calculate the probability of the temperature lying in-between the values $281K$ and…
Libor Zachoval
  • 353
0
votes
1 answer

is a cumulative distribution function (cdf) for some fixed number k . Find: k

Recall that the "floor" of a real number x , denoted ⌊x⌋ , is the largest integer ≤x $$F(x)= \left\{ \begin{array} \\ k-\frac{1}{\lfloor x\rfloor}, x\ge 1,\\ 0, x\lt 1,\end{array} \right.$$ is a cumulative distribution function (cdf) for some…
ritul 26
  • 95
0
votes
1 answer

Distribution of interval that contains N independent variables

N independent random variables are uniformly distributed on [0,1]. What is the distribution function of length of minimal interval that contains all of them?
Al.1
  • 81
0
votes
1 answer

Over a weekend of 2 days, it is given that 3 requests are received. Find the expected total income for the weekend.

A small hire company has 2 buses. Each bus can be hired for one whole day at a time. The rental charge per day is RM 600 per bus. The number of request to hire a bus for one whole day may be modelled by a Poisson distribution with mean 1.2. Over a…
user9803530
  • 63
0
votes
1 answer

Trouble Creating Joint PMF from single RV PMFs

I am working through an old college book (Probability & Statistics for Engineering and the Sciences). I came across the following problem and gave myself the extra challenge of creating the entire joint pmf. My problem is that my numbers are not…
Epsilon
  • 3
0
votes
2 answers

Joint density of random variables

$f_{X,Y}(x,y) = \frac{(xy-2x-2y+4)}{32}$; $2\le x \le y \le 6$ for random vars $X$ and $Y$; find $P(X \gt 3 \mid Y = 5)$
user207558
  • 98
0
votes
0 answers

Bernoulli distribution and Normal distribution, which is more closer to uniform distribution?

For Bernoulli and normal distribution, I'm wondering which distribution is more closer to uniform distribution. Is there any notion of similarity between two probability distributions? If so, is that a proper way to know which distribution is more…
mallea
  • 829
0
votes
0 answers

Expected value of maximum of absolute values of two independent and identicall distributed standard normal random variates

If $X_1$ and $X_2$ are independent, having both standard normal distribution, what is $E\left(\max(\left|X_1\right|,\left|X_2\right|\right)$? Actually, holding similar condition there is no problem when calculating $E(\max(X_1,X_2))$. Since…
Hamid
  • 11
1 2 3
…
99 100