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minggx

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Theorem (Mean Absolute Deviation and Mode) . Let X ~ Bin(n,p).  Let v denote the smallest integer > np and let m=©¸ np + p ©¼. Then,
(a) E|X-np|= 2v (1-p) P(X=v).
(b) The mode of X equals m. In paricular, if np is an integer, then the mode is exactly np; if np is not an integer, then the mode is one of the two integers just below and just above np.
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Originally posted by minggx at 2010-09-15 18:03:54:
ÒÔÏÂÂÛÊöÖÐ ©¸ ©¼ µÄº¬Ò壿
Theorem (Mean Absolute Deviation and Mode) . Let X ~ Bin(n,p).  Let v denote the smallest integer > np and let m=©¸ np + p ©¼. Then,
(a) E|X-np|= 2v (1-p) P(X=v).
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minggx

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ÕâÊÇA. DasGupta дµÄFundametal of Probability: A first Course, Springer, 2010 ÖеÄ99Ò³µÄTheorem 6.3 .  °ÑËüµÄÖ¤Ã÷Ҳд³öÀ´£¬×ö³ÉͼƬ£¬ ´ó¼Ò°ïÎÒÔÙ¿´¿´£¬ лл£¡
http://cid-8d349205ac2b2441.offi ... blic/Theorem6-3.bmp
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