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5 (4311) Let the random variable Z nhave a Poisson distribution with parameter = n Show that the limiting distribution of the random variable Y n= (Z n n)= p nis normal with mean zero and variance 1 Answer M Z n = en(et 1) We have that the moment generating function M n(t) of Zpn n n is M n(t) = Ee tZnp n n = e p nM(t= p n) = e p e (et. ñ ± ª E P p ¢ è s r t F p 7 G Þ t 0 b w p z p ¢ è ¢ x è ~ ì æ 0 £ s r w õ > t 7 & p b { h q Q y z S æ 0 t \ l h ï Þ Ç 7 Z z$0 ° = x É ® p $ t Z ` b { h z Ð g U É ` M F Y p z > w 9 S ê S ¤ ¯ ï p Ð T ` h 0 º w í > t Ù n Z o T w p z ä >. ١٤٢٤ Y z p « Y ` l p « Y ½ w١ / ¥ v « ¹ ² ¯ ½ v À Z ¿ ª ^ ¤ d ٨ § ½ ¢ ë § ½ ¢ Ç ¨ ø þ ó ¥ ، ¢ ½ ¢ ÿ ﹰ ¢ ﹰ ¦ û ö ô ó.
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Title Thank you for supporting us Author SHAROND Created Date 11/2/18 PM. Calculate the probability you entered from the ztable of p(z 15) The ztable probability runs from 0 to z and z to 0, so we lookup our value From the table below, we find our value of Since that represents ½ of the graph, we add 05 to our value → 05 p(z 15) = Ztable scores are below.
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