- #1

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- TL;DR Summary
- Does a given property of a random variable also apply to the sum of that variable?

For a random variable T

SD (T

with SD (T

SD (T) / E (T) ≤ 1

where T = T

_{i},SD (T

_{i}) / E (T_{i}) ≤ 1with SD (T

_{i}) = (Var (T_{i}))^{1/2}and E (T_{i}) the expectation of T_{i}and Var (T_{i}) the variance of T_{i}. My question now is whether the following property then also applies. For any variable T,SD (T) / E (T) ≤ 1

where T = T

_{1}+ T_{2}+ ... + T_{N}and where N can be a fixed variable or random variable.