Questions tagged [sum]
The sum of two or more random variables.
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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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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 ...
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Central Limit Theorem for square roots of sums of i.i.d. random variables
Intrigued by a question at math.stackexchange, and investigating it empirically, I am wondering about the following statement on the square-root of sums of i.i.d. random variables.
Suppose $X_1, X_2, ...
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How do I find the conditional distribution of a normal r. v. z, given that I know the sum of z and another normal r. v. x is greater than some value?
Suppose I have two independent normal random variables, $X$ and $Z$ with $\mu_x$, $\sigma^2_x$ and $\mu_z$, $\sigma^2_z$. Suppose I also know that $x+z\geq y$. How do I find the conditional ...
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What does it mean if the median or average of sums is greater than sum of those of addends?
I'm analyzing the distribution of network latency. The median upload time (U) is 0.5s. The median download (D) time is 2s. However, the median total time (for each data point, T = U + D) is 4s.
What ...
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Finding the distribution of sum of Lognormal Random Variables
I am trying to find the distribution of sum of 2 lognormal random variables. I referred the literature available on Cross validated, Stack overflow and few papers before posting this.
I used ...
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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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Sum of 2 Normally Distributed Random Variables With a Correlation
I've been given a problem where I have
$$
X \sim \mathcal{N}(\mu = 2, \sigma^2 = 9)
$$
$$
Y \sim \mathcal{N}(\mu = 3, \sigma^2 = 4)
$$
Their correlation is $ \rho_{XY} = 0.6 $. First I am asked for ...
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Conditional probabilities of the parameters
I have the following function
$$ x(k) = \sum_{m}^{M} e^{i(U_m k + \beta_m)} $$
Where
$$ i = \sqrt{-1} $$
The $U_m$ values come from a normal distribution and the $\beta_m$ values come from a uniform ...
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Noise cancels but variance sums - contradiction?
I have been told both things with regard to e.g. summing noisy time series, to justify opposing expectations.
On the one hand, I have been told to expect that summing multiple noisy inputs should lead ...
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Front-Door Adjustment formula: confusing notation
Pearl et al. "Causal Inference in Statistics: A Primer" (2016) p. 69 Theorem 3.4.1 provides the Front-Door Adjustment formula:
$$
P(y | \text{do}(X = x)) = \sum_z P(z | x) \sum_{x'} P(y|x', z)P(x').
$$...
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PDF of sum of truncated exponential distribution
Let $x_i$ represent samples from a Truncated Exponential distribution between $0$ and $1$, with rate parameter $\lambda$.
Defining
$\tilde x = \dfrac{\sum_{i=1}^{n}x_i}{n}$
What is the PDF of $\...
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Generate identically distributed dependent normal random numbers with prespecified sum
How do I generate $n$ identically distributed but not independent normal random numbers such that their sum falls within a prespecified interval $[a,b]$ with probability $p$?
(This question is ...
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If X=Y+Z, Is it ever useful to regress X on Y?
If we have X and Y that are mathematically dependent: X = Y + Z, is it 'forbidden' to use Y as a predictor to X in linear regression? I'm trying to find a concise explanation for why it is, or isn't.
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Measuring share contribution of each var/cov term to the standard deviation of a sum of variables
Say, for a simple example, I have a random variable $X = \alpha_1 X_1 + \alpha_2 X_2$, where $X_i$ are random variables and $\alpha_i$ are weights. I then calculate the standard deviation of $X$ as $\...
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