<t>This is a multi-part question from Michael Steele's book.a) Let V be a multivariate Gaussian column vector with mean and covariate , and let A be an n x n real matrix. Show that AV is a multivariate Gaussian vector with mean and covariance . b) Show that if X and Y are independent Gaussians with ...

<t>ah, indeed! an elegant argument.QuoteOriginally posted by: wileyswwill0t5, i was thinking of reductio ad absurdum by assuming E[n] < infty, then by Wald's equation, E[S_n]=E[X]*E[n]=0, however, y<=S_n<y+1 by the stopping criteria, thus contradiction when y>0.(actually looking at your argument, si...

I believe this is implicitly incorporated when I computed the total vacancies. I think what bakait missed, as FritzJacob pointed out, is the order of filling the 100 people in the 100 hotels (100!). QuoteOriginally posted by: dunrewppbakait fails to incorporate the capacity of each hotel.

<t>I agree with wileysw and dunrewpp that the average number of steps is infinite for y>-1. I'm not sure, however, how Wald's equation would fit in here. The following is my reasoning via martingale. First we do the simple case of y>0Suppose we keep stepping until our position s>y or s<-z. We win wh...

I'm following the logic of bakait:P(no hotel vacant)=q;Leta=# of ways to choose 100 peopleb=# of ways to put 100 people in 100 hotelsc=# of ways to put 19000 people in 50400 vacanciesn=#of ways to put 20000 people in 50500 vacanciesP(at least 1 vacant)=1-q