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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 study a distribution that is not identically distributed?

My distribution histogram looks like it is not identically distributed, as in the negative counts have a different shape than the positive counts. Here is an image: The chart has 800 data points, and the tallest count of 40 is for 0. I don't know a…
d l
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Calculating the density function $f_X$ from joint density $f_{X,Y}$

X and Y have continous distribution, the joint distribution is $f_{X,Y}(x,y)=\frac{1}{2\pi\sqrt[]{1-p^{2}}}e^{-\frac{1}{2(1-p^2)}(x^2+y^2-2pxy)}$, ($p$ is a constante) We need to find the marginal densiety $f_X$ of X. I know we have to…
Anabella Woud
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Finding a CDF given a PDF using summations

I am in a prob and stats class and we have just begun our discussion on discrete random variables. I am given a pdf of $$ f(x) = \left\{\begin{aligned} &x/10 &&: x = 1,2,\ldots,4\\ &0 &&: \text{otherwise} \end{aligned} \right.$$ I need to find an…
user219081
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Probability of Playing Darts

We have a dartboard with radius $1$, the dart will always hit the dartboard. The hitting point of the dart is uniformly distributed, with a stochastic vector $(X,Y)$. Now I want to determine the probability mass and density function. Say…
iJup
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What is the distribution of the dot product of two vectors of unit length with nonnegative elements

Let $X = A \cdot B$, where $A$ and $B$ are unit length vectors with $m$ elements, and no element of $A$ or $B$ is negative. What is the distribution of $X$? If it helps, we can assume that the elements of $A$ and $B$ both started off as Gaussian…
ken
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$X$ and $Y$ have Joint density, what is $c$?

Suppose $X$ and $Y$ have joint density $f(x,y)=c(x+y)$ for $0
iJup
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Probability of long identical substring

You have a string of $20,000$ consecutive bits. Each bit is either a $1$ or a $0$ and has a $0.5$ chance of being either. Calculate the probability that there is at least one substring of at least $34$ consecutive $1$'s or $0$'s. its not a binomial…
mitzy
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How do I find the marginal probability density function when the interval is dependent of one of the variables?

I'm trying to find $f_x$ and $f_y$ given a joint probability distribution $$f(x,y) = \frac18 (y^2 -x^2)e^{-y}$$ defined on the interval $0 \leq y \leq \infty$, $-y \leq x \leq y$ Naturally I've tried integrating on the intervals and found: $$ f_x(x)…
kaslusimoes
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Calculate Probability of a Range of Dice Rolls given their Distribution

I'll prefix this with - I'm not particularly great at Maths, so I might ask for an explanation of some of the answers. What I'm trying to do is convert this into something I can code. I've got a distribution of probabilities for dice rolls that I've…
Ian
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What will be the pdf from Mixture of Gaussians

In Euclidean $R^M$ space, I want to compute the pdf of the Euclidean distances between $d^M(\mathbf{z_i}) $= $||\mathbf{z_i -z_j}||^M = r_i^M , i \neq j$. What will be the pdf $f(r)$ ? Let there be two vectors $\mathbf{x} = \{x_i\}_{i=1}^N$ and…
Ria George
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PART TWO: Poisson counting process, probability system errors divided in time periods at a certain rate

I've been trying to apply the same knowledge from a previous post, but perhaps my reasoning is wrong. "Errors in a computer surfaces according to a Poisson process with rate 0.4 per day. If there has surfaced three errors during 15 days, what is…
DOGOFWALLSTREET
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Poisson counting process, probability system errors divided in time periods at a certain rate

I had some help on a previous post where I learned that The distribution of $X(t)-X(s)$, for $s \frac{e^{-\lambda(t-s)}(\lambda(t-s))^k}{k!}.$$ Now the question is…
DOGOFWALLSTREET
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U,V are two independent random variables each with the uniform distribution on $[0,1]$. What is the $P(V^2 >U>x)$?

$U$, $V$ are two independent random variables each with the uniform distribution on $[0,1]$. Show that $P(V^2>U>x)$ is $1/3 -x +2/3x^{2/3}$ for $0U)$.
guest10923
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A Continuous random variable X has probability density function $f(x)=ae^{-ax}$

A Continuous random variable X has probability density function $f(x)=ae^{-ax}$ where I found $a=0.5ln2$ I Found that the mean of this distribution occurs at X=2. Now, I was then asked what is: P(X<3) given P(X>1) Can someone explain why this is…
user2250537
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What is the maximum of $n$ points with CDF $F$ and PDF $f$?

I read somewhere that the minimum of $n$ points with CDF $F$ and PDF $f$ is $g(y) = n(1-F(y))^{(n-1)}f(y)$ What would the corresponding maximum value of the points be? Also, how do we derive the minimum and maximum values?
saikat
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