How to expand:
$E(Y+1)^2$
my working out:
$E(Y^2)+E(1^2) = E(Y^2)+1$ (I'm not sure why this is though..)
Can someone link to or list the rules for expanding the expected value ......
2026-04-01 03:30:04.1775014204
Expanding the expected value
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Since $(Y+1)^{2}=Y^{2}+2Y+1$ we have $$E[(Y+1)^{2}]=E[Y^{2}+2Y+1]$$ where by properties of linear expectation we have $$=E[Y^{2}]+2E[Y]+1$$ also since $Var[Y]=E[Y^{2}]-(E[Y])^{2}$ we can also write this as $$=Var[Y]+(E[Y])^{2}+2E[Y]+1$$