All Questions
Tagged with sum convolution
10
questions
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PDF of difference of uniform distributions [duplicate]
Main questions are in bold but feel free to correct me if I'm wrong somewhere else. As far as possible, I need both intuition and formal explanation.
Let $X \sim Uniform(a,b)$ and $Y \sim Uniform(c,d)$...
25
votes
4
answers
2k
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Probability that sum of binary variables is even
Let $S_i \in \{0,1\}$, $i=1,\dots,N$ be $N$ independent random binary variables, each taking the value 1 with probability $0 \le p_i \le 1$ (and the value 0 with probability $1-p_i$).
I am interested ...
- 4,440
2
votes
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49
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Estimating the distribution of a sum of two random variables if the family of one of the variables is known
Assume I have a random variable $Y=X_1+X_2$. I want to estimate the distribution $f$ of $Y$ given a sample $y_1,\ldots,y_N$. If this was all that is known about $Y$ the best way would probably be to ...
- 2,671
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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
2
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81
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When is $\sum Z_i \sim \sqrt{n} Z_i$?
If $X_i$ are independently and identically distributed $N(0,\sigma^2)$ then $Y=\sum X_i \sim N(0,n\sigma^2)$, i.e. $\sum X_i \sim \sqrt{n}X_i$. That raises two questions:
Is a zero-mean normal ...
- 40.5k
3
votes
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82
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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
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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
2
votes
1
answer
65
views
Force sum of random varables to equal to 1 [duplicate]
Suppose I have 3 random variables, $X1, X2,X3$. Define $Z$ as:
$Z=X1+X2+X3$
I want to force $Z$ to equal 1 for every "realization" of $X1,X2,X3$ ($X_i \sim Beta(a_i,b_i))$. As an example, let $X_i$ ...
- 163
8
votes
1
answer
720
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Finite sum of beta prime iid random variables
The beta prime distribution is infinitely divisible, as proved in Steutel and van Harn, 2003 (Appendix B). Sadly, in this book, there is no expression of the parameters of the distribution of $n$ ...
- 183
26
votes
4
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44k
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The sum of independent lognormal random variables appears lognormal?
I'm trying to understand why the sum of two (or more) lognormal random variables approaches a lognormal distribution as you increase the number of observations. I've looked online and not found any ...
- 1,779