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٧ Y XW V U T S R Q P O N M L f e d c b a ` _ ^ \ Z q p on m l k j i h g ٨ g f e d c b a ` _ ^ \ r qp o n m l k j i h ~ } { z y x wv u ts. Proof of part c As in part b of theorem 1, write S2 as a function of the sum of square of Xi minus n times the mean of Xisquared and then simplify ES2 = E 1 n− 1 " i=1 X2 i − nX¯2 #!. @ ̓ ́A C X G Q j A ݂̂U O ̓y n ɕ 邱 Ƃ Ӗ Ă B C X G ݕ Ɍ Ă 邱 Ƃ͈ȑO 犴 A R ɋL ɂ B ݕ ̐ \ A g v ̋ a } e ̒ ł 邱 Ƃ d v B ݂ ` a b ̂R n ɋ敪 ̂͂X T N ̃I X ӂŁA ` Ƃa p X ` i l ̐l W n i ` ̓p X ` i { ̎ n A a ͎ { ƃC X G R ̋ Ǘ j ŁA ȊO b B p X ` i l ̑唼 i Q W O l j ͂` Ƃa ɏZ ł 邪 A ` a ͔ є тɑ ݂ A s s Ԃɂ b.

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C Continuous case For a continuous variable X ranging over all the real numbers, the expectation is defined by µXE(X) = ∫xf(x) dx = ∞ ∞ D Variance of X The variance of a random variable X is defined as the expected (average) squared deviation of the values of this random variable about their mean That is, µ µ σ2. E C X g ̓W A ̂ ē Ȃǂ J Ă ܂ B @ Ō i q ̃o X P A y \ i4 A V E e j X ̉ q l ARAGNAROK ONLINE A j. á ç\î þ \ü å \Ã\õ\É\ë \Õ\Ó\ý\Ô ß\î Ö o 5 ö.

ì Ó Ô f þ 2 k µ Q ç Ó * à J ' í & J A Ë · * % @ I ¹ µ » a C x @ & Ó * · Æ ê À C Q Ë · J ' í. H % ù. = 1 n −1 nEX2 1 −nEX¯2 = 1 n −1 n(σ2 µ2)−n σ2 n µ2 = σ2 (21) The last linefollows from the definitionof the variance of a random.