Hw4 - 2 3#4 f n^ a f(r t f.l ^7lA-a/dd 7t HVdl,l =1 l...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
2, 3.#4 ; f, )" +^7lA/-a-//dd 7t/ HVdl a/. f(r .l - Wr'r.fuh* =1/ ;r./ 3 /,/- t f \ n^/ l- -l)o. ( il^totG)"-'+-. rt* *,/e*); ,l (rt)' 2.3.L2. P[at least 3] : 2.3.13.(SA)Thep.m.f.forthegeometricdistributionwithSuccesspa- rameter p it * follows: s(t) = (I - p)^-Lp' Therefore' F(n) :p(1 + (1 - p) + (r - p)2+ "' + (i - p)n-t) Thisisageometricserieswith":(1_p)whichislesstharrl,whosesum is pH. Substituting (1 - P) for r' r' ' 1- (1 -P)' r(n):n-ffi:1-(1 -P)*- I Therefore r J f(" + -; : (1 -P)"*4 | : (t-F(n))(t-r(*)). 1-F(n*rn)givesthetotalprobabilitythatthefi'rstn*rntrialsare failures. This is .q"J ao the product of the probability that the first n trials are failures'J"J ,n" probabitity that the first nr' trials are failures' This equality lIr"r.o lt "lu- thut failing on the first n. trials. does not af- fectfailingonthenextrntrialsinanyway.Theoutcomeofeachtrialis . independent of the outcomes of the previous ones' 2'3'15. The random variabre counts the number of triars untir the third success, hence it has the negative binomial p.m.f. /* ] t) f+)'f:)*-', * :3,4,b,... \ z /\t) \A/ rn:rr4,b,...
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern