# [R] Recommendation on a probability textbook (conditional probability)

Ista Zahn istazahn at gmail.com
Sat Oct 17 04:14:35 CEST 2009

On Fri, Oct 16, 2009 at 9:37 PM, Peng Yu <pengyu.ut at gmail.com> wrote:
> What's the title?

Introduction to Probability.

>
> 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
>>> http://www.R-project.org/posting-guide.html
>>> and provide commented, minimal, self-contained, reproducible code.
>>
>>
>>
>> --
>> Yi Du
>>
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> and provide commented, minimal, self-contained, reproducible code.
>

--
Ista Zahn