1.Let the PDF of X be given by F(x)=0.25exp(-0.25x),x>0.Show that E(x)=4 and var(x)=16. 2.Given that the random variable W is binomial distribution with b trials and success probability P is each trial and p(W=w)=h(w),show that  (a).h(w)/h(w-1)=p(n-w+1)/(1-p),w>0 (b).E[W(W-1)]=n(n-1)P^2 (c).E(1/W+1)=1-(1-p)^n+1/(n+1)P.

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.