Questions tagged [sum]
The sum of two or more random variables.
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For k independent variables, if each one is independent of $Y_1$,...,$Y_p$, how to formally prove their sum is also independent of each $Y_p$?
SUppose I have $X_1,...,X_k$ independent of each other. I also have $Y_1,...,Y_p$ is independent of each other. If each one in $X_1$,...,$X_k$ is independent of each one in $Y_1$,...,$Y_p$, how to ...
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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 ...
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Consistency when we want to find the distribution of sum of random variables following each one a distribution
I want to clarify a point that disturbs me among different cases.
I am interested in formulate correctly in a general case when we know the distribution of different random variables and we want to ...
user226073
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How do I sample Simultaneous Sums of Gamma-Distributed Variables?
Suppose I have 7 variables $y_i$ sampled from $Gamm(a,1)$, with $a>0$. Now, I define
$$x_1 = y_1+y_2+y_3+y_4,$$
$$x_2 = y_1+y_2+y_5+y_6,$$
$$x_3 = y_1+y_3+y_5+y_7$$
What is the distribution of $x_1$...
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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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Numerical evaluation of infinite sums
I am working with Skellam random variables and I would like to evaluate the CDF of the absolute value of a Skellam random variable in which both Poisson random variables have the same rate, $\lambda_1 ...
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How is a convex combination of Dirichlet-distributed variables distributed?
Let $X = (X_1, \dots, X_K) \sim \operatorname{Dir}(\alpha_1, \dots, \alpha_K)$ and define the convex combination $Y = \sum_{i=1}^{K} c_i X_i$.
In the case of $K=2$, the constraint $\sum_{i=1}^{K} X_i =...
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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 ...
user226073
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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 ...
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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....
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Is the sum of 3 bits a linearly separable task?
In other words can a linear classifier learn to correctly assign a class (label 0 to 3) for an input of 3 bits? Intuitively this cannot work, since the half-adder circuit contains an XOR block, which ...
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Sum of a number of shifted exponentially distributed random variables
I know that the sum of $k$ independent exponentially distributed random variables each with density function:
$$\displaystyle \lambda\,{{\rm e}^{-\lambda\,x}}$$
has an Erlang distribution:
$$\...
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Expectation of Maximum and Minimum of Partial Sums of Normal Random Variables
Peggy Strait, 1974, Pacific Journal of Mathematics
ON THE MAXIMUM AND MINIMUM OF PARTIAL SUMS OF RANDOM VARIABLES
Gives a nice result (4.3) and (4.4) in terms of "standard normal random variables&...
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What is an intuitive explanation for Q90 (X+Y) > Q90(X) + Q90(Y) in fat-tailed variables. Non Subadditivity
In a business situation, management keeps a reserve of money for a 'rainy day' just in case costs are more than expected. The 90th percentile ($Q_{90}$ in the following) might be an indicator of how ...
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