[R] 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.
__
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Re: [R] Recommendation on a probability textbook (conditional probability)
What's the title?
On Fri, Oct 16, 2009 at 8:16 PM, Yi Du abraham...@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...@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.
--
Yi Du
__
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.
Re: [R] Recommendation on a probability textbook (conditional probability)
On Fri, Oct 16, 2009 at 9:37 PM, Peng Yu pengyu...@gmail.com wrote:
What's the title?
Introduction to Probability.
On Fri, Oct 16, 2009 at 8:16 PM, Yi Du abraham...@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...@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.
--
Yi Du
__
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.
Re: [R] Recommendation on a probability textbook (conditional probability)
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.
