Hw4 - 2, 3.#4 ; f, )" n^/ a/. f(r t f \ .l -...

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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
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Hw4 - 2, 3.#4 ; f, )" n^/ a/. f(r t f \ .l -...

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