Linked Questions

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0answers
369 views

Sum of N random variables from the same distributions [duplicate]

Given $n$ independent random variables from the same distribution, how to obtain the distribution of their sum? For example, the distribution of $n$ normal distribution is $N(n\mu, n\delta^2)$. ...
2
votes
0answers
120 views

Sum of Discrete Random Variables [duplicate]

If I have two independent discrete random variables, say, $$ X \in \{1,3,10,20\} $$ and $$ Y \in \{2,3,5,9,11,15\} $$ and let $$Z = X + Y $$ be the sum of two variables. Also, each value taken by ...
0
votes
1answer
55 views

Why use Convolution of probability function instead of cross-correlation? [duplicate]

First, let me quickly remind you of the two operations: convolution and cross-correlation between 2 function $f$ and $g$, assuming continuous domain. Cross-Correlation $f \star g$ : $\int f(\tau)g(\...
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0answers
17 views

Derive the CDF of the sum of two independent random variables [duplicate]

Some notational remarks before presenting the question: $k<\infty$, with $k\in \mathbb{N}$. $\lambda\equiv (\lambda_1,...,\lambda_k)$, $\lambda_j\in [0,1]^k$ $\forall j$, and $\sum_{j=1}^k\...
1
vote
0answers
12 views

Independent and Identically distributed random variables with value at risk [duplicate]

Suppose that $W_1$ and $W_2$ are i.i.d. and $P(W_i>x)=x^{-1/2}$ and $x$ is greater than or equal to $1$ and $i=1,2.$ How do you show that $P(W_1+W_2>x)=(2\sqrt{x-1})/x$? I know it involves ...
71
votes
8answers
11k views

What is meant by a “random variable”?

What do they mean when they say "random variable"?
37
votes
4answers
18k views

Generic sum of Gamma random variables

I have read that the sum of Gamma random variables with the same scale parameter is another Gamma random variable. I've also seen the paper by Moschopoulos describing a method for the summation of a ...
21
votes
4answers
4k views

Can anyone clarify the concept of a “sum of random variables”

In my probability class the terms "sums of random variables" is constantly used. However, I'm stuck on what exactly that means? Are we talking about the sum of a bunch of realizations from a random ...
10
votes
2answers
1k views

Why does convolution work?

So I know that if we want to find the probability distribution of a sum of independent random variables $X + Y$, we can compute it from the probability distributions of $X$ and $Y$, by saying $$f_{X +...
2
votes
2answers
552 views

Distribution of values in a time series (tidal data)

I was trying to help my colleague with fitting a distribution curve to some empiric data (these are sea water level observations at different time points). However, I haven't succeeded since it's my ...
3
votes
3answers
47 views

Question about random variables and the distribution of the sample mean

I'm new to statistics. I am so confused as to why the Xbar (the random variable describing the sample mean) can be found by taking the average of all the X's. From what I understand the capital X's ...
3
votes
3answers
90 views

What does the minimum of a random variable mean?

Let $X_1, X_2, X_3, \cdots,X_n$ be independent and identically distributred (iid) random variables. Then, how would you know/calculate what $min(X_1, X_2, X_3, \cdots,X_n)$ is?
8
votes
1answer
170 views

Do random variables follow the same algebraic rules as ordinary numbers?

In the comments on my answer to a recent question about the sum of random variables, I came across a link to the Wikipedia article on the ratio distribution, and noticed the following peculiar claim ...
3
votes
1answer
169 views

How does the maximum distance between adjacent values vary for increasing $n$

That is, when is the $\underset{n \to \infty}{\lim} \max (X_i-X_{i-1})\rightarrow 0$, where $1<i\leq n$, and $X_i\geq X_{i-1}$ and when is the limit $\neq 0$? The question supposes that the ...
2
votes
1answer
166 views

What is the distribution of the difference between two random numbers?

I have a big bag of balls, each one marked with a number between 0 and $n$. The same number may appear on more than one ball. We can assume that the numbers on the balls follow a binomial distribution....

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