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= 1 x 1 x2 1·2 x3 1·2·3 ··· • For large x > 0, ex > x p p!. ä ä n g > b > = \ x p d @ k d p g _ r d r = q r \ r i x k p n m s a c k h ä ' ä g = t x k \ a m s x y w v { x v {. Kb) p(x k) = a sum{x kp(x k)} b sum{p(x k)} = aE(X) b Variance We often seek to summarize the essential properties of a random variable in as simple terms as possible The mean is one such property Let X = 0 with probability 1 Let Y = 2 with prob 1/3 1 with prob 1/6.

í î ï ð ˆ ‹ › æ ò ó ô ı ö ÷ î?. Links with this icon indicate that you are leaving the CDC website The Centers for Disease Control and Prevention (CDC) cannot attest to the accuracy of a nonfederal website Linking to a nonfederal website does not constitute an endorsement by CDC or any of its employees of the sponsors or the information and products presented on the website. Æ Ê Ë Ì Í Î ½ · Ï ¹ µ º Í Ð Ñ ¹ Æ Ò µ Ó ¶ Ñ Ñ Ô ¸ Å Õ ´ ¹ ¸ Å Ç Ö × ¸ µ ¼ Ä ¸ · ¹ · Ñ Ø ¹ Ò ¸ Ù ¹ Ô Ú Û ¼ ³ Â À Á Ü · µ Ý ¹ µ ¶ Ó Í Ò Ç ¹ Ò Ø Ú Û Ë ¼ ³ ½ Â Ê À Á Ì Å Î Þ ¹ Ó Å Ù Ï ¹ · Ñ Ñ Ô ´ Æ º Ð Ñ ¹ Æ ß Ó Ì Ô Î ³ Ò Í Ð Ñ ¹ Æ µ.

Title Microsoft Word Iniciacao_Aula6_Dumbotaotantodocx Author Utilizador Created Date 4/22/ 1505 AM. X k z ð ± 4 « B « C ¾ ª þ Ë þ Á â x k z ð ± * 1 ª þ Q Ã ' % å · ù * Q ð ± « è þ ¯ * â i k x @ ¨ s x k z Ì ½ Ð É % ò y ¸ É b Æ ¨ º ¨ b à Ë > É à å þ Æ Ù ´ æ Ì I h s ª þ Ë å m ¥ q 4 * % À ò s 4 Q !. Ae 3 tBe5 This will decay at inﬁnity only if B 0 Now, evaluating x and x at 0 gives us the equations (1215) x 0 A B x 0 3A 5B Setting B 0, the condition becomes x 0 3x 0 0 Case of complex roots If the discriminant a2 4b 0, then the roots are two complex conjugate numbers α iβ α iβ Let’s ﬁrst look at the case y y 0.

Xk i=1 X i = Xk i=1 EX i (by linearity of expectation) = Xk i=1 1/p (since X i ∼ geom(p)) = k/p 5 (MU 218;.