# Questions tagged [sum]

The sum of two or more random variables.

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### Probability of a sum of random variables falling in a given range

Given a distribution $P$, two values $a$ and $b$, $x=0$, and the following process: Draw a number $r$ from $P$ and add it to $x$, this is $x = x+r$. Keep doing this until $x$ is higher than $a$. ...
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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 $\left(f_X(x) = 2e^{-2x}\right)$, ...
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### How to apply Lyapunov CLT to data

I have a situation where I have around 30 classes of variables with different means and variances (though the means aren't too far from eachother; think 4-7) and that the distributions are right ...
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### 2 approaches for Monte-Carlo : weighted sum of $\chi^2$ distribution and Moschopoulos distribution with Gamma distribution

If I take as definition of $a_{lm}$ following a normal distribution with mean equal to zero and $C_\ell=\langle a_{lm}^2 \rangle=\text{Var}(a_{lm})$, and if I have a sum of $\chi^2$, can I write the 2 ... 1 vote
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### Probability that any element of a random unit-length vector is large [closed]

Given a vector $X \in R^n = \{x_1, x_2, ..., x_n\}$ drawn uniformly such that: $x_i \in [0, 1]$ for all $i$; and $\sum x_i = 1$, how would you find the probability that any of the $x_i > y$, for ...
### If $20$ random numbers are selected independently from the interval $(0,1)$ probability that the sum of these numbers is at least $8$? [closed]
If $20$ random numbers are selected independently from the interval $(0,1)$ what is the probability that the sum of these numbers is at least $8$? I tried to take this question https://math....