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Jan 24 at 20:06 comment added Iosif Pinelis @AaronHendrickson : Yes, the variance of $T$ taking values in any interval $[a,b]$ is maximized, for any given mean value of $T$, when the values of $T$ are at the endpoints. One way to see this is to consider the random variable $S:=T-a$, taking values in the interval $[0,b-a]$, with $ES=ET-a$ and $Var\,S=Var\,T$.
Jan 17 at 20:52 history edited Iosif Pinelis CC BY-SA 4.0
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Jan 17 at 20:29 vote accept Aaron Hendrickson
Jan 17 at 19:37 history edited Iosif Pinelis CC BY-SA 4.0
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Jan 17 at 19:29 history answered Iosif Pinelis CC BY-SA 4.0