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Upper bound of two binomially distributed random variables
Let be $X_1,X_2$ two i.i.d binomially distributed random variables, where $p$ is the probability of success and $m$ the length of the underlying Bernoulli experiment. In a proof our professor argues
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Upper bound for Variance of linear combination of random variables: $\operatorname{Var}\left(x^Ta\right) \leq \frac{\|a\|^2}{4}. $
I found this while reading a paper where they used it as a casual fact.
Say, you have a vector $x = (x_1, x_2, \dots, x_n)$ where $x_i \in [0,1]$ are independent random variables. Consider linear ...
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