I guess it's just me being dumb but I really don't get this, even with the formula put right out in front of me.
Edit: I thought it would make sense that I just sum up p(1)\times\cos(\pi 1/2)+p(2)\times\cos(\pi 2/2)+p(3)\times\cos(\pi 3/2)+p(4)\times\cos(\pi 4/2)
... which (I think) would...
Homework Statement
A card is drawn at random from an ordinary deck of 52 cards and its face value is noted, and then this card is returned to the deck. This procedure is done 4 times all together. Let X be the total number of aces selected and Y = \cos(\pi X/2).
E[Y] = ?
Homework Equations...
I was in the midst of doing that, but wasn't sure if I was allowed to say
"since a < b, a^{2} < a \cdot b
similarly, \sqrt{a^{2}} < \sqrt{a \cdot b} "On top of that, I get stuck when trying to prove the "middle" part: \sqrt{ab} < \frac{a+b}{2}
Homework Statement
Prove that if 0 < a < b, then
a < \sqrt{ab} < \frac{a+b}{2} < b
Homework Equations
Axioms (Properties), courtesy of Wikipedia:
Addition:
P1: For all a, b, and c in F, a + (b + c) = (a + b) + c
P2: There exists an element of F, called the additive identity...