There are many examples in the book. Since I'm refreshing my memory. Is there a more concise one?
On Fri, Oct 16, 2009 at 8:26 PM, Ista Zahn <istaz...@gmail.com> wrote: > I like Grinstead and Snell, not least because it's free: > http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/book.html > > -Ista > > On Fri, Oct 16, 2009 at 9:12 PM, Peng Yu <pengyu...@gmail.com> wrote: >> I need to refresh my memory on Probability Theory, especially on >> conditional probability. In particular, I want to solve the following >> two problems. Can somebody point me some good books on Probability >> Theory? Thank you! >> >> 1. Z=X+Y, where X and Y are independent random variables and their >> distributions are known. >> Now, I want to compute E(X | Z = z). >> >> 2.Suppose that I have $I \times J$ random number in I by J cells. For >> the random number in the cell on the i'th row and the j's column, it >> follows Poisson distribution with the parameter $\mu_{ij}$. >> I want to compute P(n_{i1},n_{i2},...,n_{iJ} | \sum_{j=1}^J n_{ij}), >> which the probability distribution in a row conditioned on the row >> sum. >> Some book directly states that the conditional distribution is a >> multinomial distribution with parameters (p_{i1},p_{i2},...,p_{iJ}), >> where p_{ij} = \mu_{ij}/\sum_{j=1}^J \mu_{ij}. But I'm not sure how to >> derive it. >> >> ______________________________________________ >> R-help@r-project.org mailing list >> https://stat.ethz.ch/mailman/listinfo/r-help >> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html >> and provide commented, minimal, self-contained, reproducible code. >> > > > > -- > Ista Zahn > Graduate student > University of Rochester > Department of Clinical and Social Psychology > http://yourpsyche.org > ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
