1. Answer the following question when X,X.X, is a random sample fromN(. o*).1(a) Find the integral generation function of S=n-1i= 1(b) Using the above results, find the limit of S when the sample size n increases.

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Answered: 1. Answer the following question when…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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1.9.5. Let a random variable $X$ of the continuous type have a pdf $f(x)$ whose graph is symmetric with respect to $x=c .$ If the mean value of $X$ exists, show that $E(X)=c$Hint: Show that $E(X-c)$ equals zero by writing $E(X-c)$ as the sum of two integrals: one from $-\infty$ to $c$ and the other from $c$ to $\infty .$ In the first, let $y=c-x$ and, in the second, $z=x-c .$ Finally, use the symmetry condition $f(c-y)=f(c+y)$ in the first.
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1. Answer the following question when X.X...X is a random sample from N(u.o). |(a) Find the integral generation function of S°= (b) Using the above results, find the limit of s° when the sample size n increases.