[R] Recommendation on a probability textbook (conditional probability)
Peng Yu
pengyu.ut at gmail.com
Sat Oct 17 03:37:20 CEST 2009
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.
>>
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>
>
>
> --
> Yi Du
>
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