R help - Oct 2009 - Recommendation on a probability textbook (conditional probability)

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.

What's the title?

On Fri, Oct 16, 2009 at 8:16 PM, Yi Du <abraham.du at gmail.com>
wrote:
> Hogg's book is enough for you considering your problems.
>
> Yi
>
> On Fri, Oct 16, 2009 at 7:12 PM, Peng Yu <pengyu.ut at 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 at 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.
>
>
>
> --
> Yi Du
>

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 <istazahn at 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.ut at 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 at 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
>