Joint probability distribution of several random variables gives the probability that all of them simultaneously lie in a particular region.
Questions tagged [joint-distribution]
860 questions
7
votes
1 answer
Joint distribution of dependent Binomial random variables
Suppose we have $X_{1} \sim B(m,p_{1}), X_{2} \sim B(m,p_{2}),\cdots, X_{n} \sim B(m,p_{n})$ and they are dependent. Does the joint distribution $f(X_{1},X_{2},\cdots,X_{n}) $ have a closed form?
Edit: let's take as an example a random graph, what's…
Toney Shields
- 882
5
votes
2 answers
Can the marginal distributions of A,C and B,C be used to build joint distribution of A and B?
There are three random variables $A$, $B$ and $C$. If the variables $A$ and $B$ were independent, their marginal joint distribution would be given by
$$
P(A,B) = P(A)P(B)
$$
For example, given the discrete probability distributions of $A = \{ A_1,…
Sakari Cajanus
- 288
5
votes
1 answer
the joint distribution of the degrees of an Erdős–Rényi graph
Does the joint distribution of the degrees of an Erdős–Rényi graph have a closed form?
Toney Shields
- 882
5
votes
3 answers
Mixed joint distribution
Let $Y = \max\{0,Y^*\}$, where $Y^*$ follows a continuous distribution. I found in the paper which I am reading that
$$
f_{Y,Y^*}(Y, Y^*) = I(Y = Y^*)f_{Y^*}(Y^*),
$$
where $I(\cdot)$ is an indicator function. I do not know how to derive this…
Kolibris
- 615
4
votes
1 answer
What does it mean to factor a joint distribution?
A book I'm reading (Hogan & Mason, 2012, p37) contains the following passage:
The joint distribution can be factored in two different ways into
conditional and marginal probabilities that reveal different aspects
of forecast quality. The…
user1205901 - Слава Україні
- 12,873
3
votes
1 answer
How do I obtain joint distribution of uniform random variables conditioned on a sum constrain?
Let us say, we have two random variables,
x1 --> U(10,20) i.e. x1 is uniformly distributed between 10 and 20, and
x2 --> U(20,40) i.e. x2 is uniformly distributed between 20 and 40.
Moreover, it has to be ensured that x1+x2 = 40 always.
How do I…
user11151416
- 41
2
votes
0 answers
distribution of a multivariate transformation with different dimensions
Given a continuous multivariate random variable $\bf X$ with pdf $f_\mathbf X$, and an invertible transformation $g:\mathbb{R}^n \to \mathbb{R}^n$, it is known that the joint pdf of $\mathbf{Y}=g(\mathbf{X})$ is given by
$$
f_\mathbf Y(\mathbf…
husB
- 121
2
votes
2 answers
Expectation of joint probability mass function
Let the joint probabilty mass function of discrete random variables X and Y be given by
$f(x,y)=\frac{x^2+y^2}{25}$, for $(x,y) = (1,1), (1,3), (2,3)$
The value of E(Y) is ?
Attempt
$E(Y) = \sum_{x,y} y\cdot\frac{x^2 + y^2}{25}$
$E(Y) =…
RStyle
- 131
- 1
- 4
2
votes
1 answer
Joint pdf problem on a general space
I came across this question in a book and having trouble understanding it.
Suppose $(X,Y)$ are continuous random vector with joint pdf $f(x,y)$ and support $\mathcal{X} \times \mathcal{Y}$. In particular suppose that the marginals $f_X(x)$ and…
user111092
- 165
2
votes
1 answer
$\prod_{j=1}^n[f(x_j;\theta))^{i_j}\pi^{i_j}(1-\pi)^{1-i_j}]=[\prod_{j=1}^n f(x_j;\theta)^{i_j}]\pi^m(1-\pi)^{n-m}$?
I would like a clarification for the following equivalence:
$$f(x_1,i_1,...,x_n,i_n|\theta, \pi)=$$
$$\prod_{j=1}^n[f(x_j;\theta))^{i_j}\pi^{i_j}(1-\pi)^{1-i_j}]=[\prod_{j=1}^n f(x_j;\theta)^{i_j}]\pi^m(1-\pi)^{n-m}$$
where $I_j\text{~}Bin(1,\pi)$…
mavavilj
- 4,109
1
vote
2 answers
How to do I find a joint density?
Can someone please help me with finding the joint density of $Y_1$ and $Y_2$ when $Y_1=X_1+X_2$ and $Y_2=X_1-X_2$?
user40275
- 21
1
vote
1 answer
Possible to store 2 dimensional distribution as a univariate distribution?
I am dealing with a dataset that has -
many "measurements" (say X, Y and Z)
a tremendous amount of data (at least considering we need to query it on the fly)
and a user base that is interested in joint probabilities of measurements (e.g. P(X >= x &…
Bi Act
- 23
1
vote
1 answer
Joint and Marginal distribution
I need to clarify something I came across in my calculations. I will appreciate any clarification or being pointed to the right literature to understand this concept.
Given the joint distribution of two random variables, $X$ and $Y$, each defined on…
BoltzBooz
- 111
1
vote
1 answer
Joint CDF of $F_{X,X+Y}$
I have a random variable $X$ and I define an additional random variable $Z=X+Y$. Now $X$ and $Z$ are dependent.
I know the distributions of $X$, $Y$ and I know that $X$ and $Y$ are independent.
In particular, for my case $X\sim Gamma(N,\lambda)$ and…
Knyq
- 53
1
vote
1 answer
How to specify joint distribution when they are not jointly independent?
I have three variables, $X, Y, Z$ with marginal distributions $F_x, F_y, F_z$.
I want to specify the joint distribution $F_{xyz}$ of $(X, Y, Z)$.
I know that if $X, Y, Z$ are jointly independent, then $$F_{xyz} = F_x F_y F_z.$$
However, what if…
contour
- 11