In_The_Wind

How about some morning discreet math problems kids

Let X and Y be independent random variables. Prove that: V (X +
Y ) = V (X) + V (Y ).
V (X+Y ) = E[(X+Y )2]��E[(X+Y )]2 = E[X2+2XY +Y 2]��(E[X]+
E[Y ])2 = E[X2] + E[2XY ] + E[Y 2] �� E[X]2 �� 2E[X]E[Y ] �� E[Y ]2.



Answer
Hence we
have E[X2] �� E[X]2 + E[Y 2] �� E[Y ]2 = V (X) + V (Y ).


True story when i was taking discreet math I told my professor the very first day that I preferred to do my math out in the open and not discreetly he didnt think that was funny needless to say it was a longgggggggg semester