All Questions
Tagged with sum joint-distribution
6
questions
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12
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What is difference between the joint probability distribution and the sum/convolution, of 2 dists? [duplicate]
Google is coming up a bit short when I searched for "joint vs sum random variables".
Perhaps someone can provide an authoritative answer to compare and contrast the sum/convolution of 2 ...
- 127
1
vote
1
answer
77
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Probability of joint dependent events
I'm having trouble finding a way to do this calculation and checking if I'm correct:
Let $X_1 \sim Exp(2)$ and $X_2 \sim Exp(2)$ be independent random variables $\left(f_X(x) = 2e^{-2x}\right)$, ...
- 113
3
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When (if ever) is the sum of two dependent geometric RVs negative binominal?
Imagine you have two random variables $X $ and $Y$, you know
$$
X \sim \text{Geometric}(p) \\
X + Y \sim \text{Negative Binomial}(2, p)
$$
I am interested in what if anything can be said about the ...
- 131
1
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51
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Independence of random variables and sums of random variables
I am seeking to find the joint distribution of X and Y. I have the marginal distributions of X and X+Y and they are independent.
We have that $f(X=x,Y=y)=f(X=x,X+Y=x+y)$ which is equal to $f(X=x)f(X+...
- 459
1
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0
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196
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Convolutions of joint random variables
I have two discrete dependent random variables $X,Y$, where both $X$ and $Y$ can take values either $0$ or $1$. Furthermore, I know their joint distribution $f_{X,Y}(X,Y)$.
Now let's say I have an ...
- 231
6
votes
1
answer
638
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Aggregation with an overlap: Dirichlet distribution
Suppose that we have $$(p_1,p_2,p_3,p_4)\sim Dirichlet(a_1,a_2,a_3,a_4),$$
where $p_4=1-p_1-p_2-p_3.$
When we add random variables for example, $p_1+p_2$ and $p_3+p_4$, the resulting distributions ...
- 433