# How to calculate the highest/smallest possible value of the variance of two random variables mean?

Two random variables $X$ and $Y$ have a common expected value $E(s)$ and a common variance $Var(s)$.

• What's the highest possible value of the variance of their mean, $var ((x+y)/2)$?

• What's the smallest possible value of the variance of their mean $var ((x+y)/2)$?

I don't know how to start :(

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 Paul - Welcome to math @ SE! it will help if you write down what you've tried so far. – nbubis Feb 5 at 11:53