Question-209027 Tinku Tara June 30, 2024 Others 0 Comments FacebookTweetPin Question Number 209027 by Spillover last updated on 30/Jun/24 Answered by Spillover last updated on 05/Jul/24 f(x)=12k+1x=1,2,3,4,5,…..nfromMomentgeneratingfunction(MGF)Mx(t)=E(etx)Mx(t)=∑nx=1etxf(x)Mx(t)=∑nx=1etx.12k+1Mx(t)=12k+1∑nx=1etxMx(t)=12k+1(et+e2t+e3t+e4t…..ent)Thisisgeometricseriesfrom∑nx=1arn−1=a(1−rn)1−ra=etr=etet(1−ent)1−rMx(t)=12k+1[et(1−ent)1−r]1stderivative=mean=Mx(t)=12k+1[et(1−ent)1−et]Mx′(t)=12k+1[et(1−ent)−etnet(1−et)2]t=0Mean(x−)=−12k+1applyquotientruleMx′(t)=ddt[12k+1et(1−ent)−etnet(1−et)2]Mx″(t)=d2dt2[12k+1.et(1−ent)−etnet(1−et)2] Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: Question-208972Next Next post: Question-209026 Leave a Reply Cancel replyYour email address will not be published. Required fields are marked *Comment * Name * Save my name, email, and website in this browser for the next time I comment.