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### 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 $N(n\mu, n\delta^2)$. ...
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### 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 ...
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### 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 ...
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### What is meant by a “random variable”?

What do they mean when they say "random variable"?
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### 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 ...
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### 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 ...
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### 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 +...
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### 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 ...
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### 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 ...
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### 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?
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### 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 ...
### 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 ...
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....