Thursday, July 28, 2011

TeXLive 2011 released!

I'm happy to know that TeXLive 2011 is available ( http://www.tug.org/texcollection/ ), and I'm currently downloading the iso image from TUG( http://www.tug.org/texlive/acquire-iso.html ).

Hopefully I'll try to install TeXLive 2011 in the weekend or next week.

Thursday, July 21, 2011

The Two Laws of Probability (Bulmer, 1979)

The Law of Addition

If A and B are mutually exclusive events, that is if they cannot both occur together, then the probability that either A or B will occur is equal to the sum of their separate probabilities:

P(A or B) = P(A) + P(B)

In general, if A and B are any two events, not necessarily mutually exclusive, the probability that A or B will occur is the sum of their separate probabilities minus the probability that they both occur:

P(A or B) = P(A) + P(B) - P(A and B)
or

P(A) + P(B) = P(A or B) + P(A and B)

#R-code Table 2(a/b)
> Table2a = rbind(c(359881, 8609), c(340454, 7796))

> rownames(Table2a) = c("Male", "Female")
> Table2a
[,1] [,2]
Male 359881 8609
Female 340454 7796


> colnames(Table2a) = c("Liveborn", "Stillborn")
> Table2a
Liveborn Stillborn
Male 359881 8609
Female 340454 7796


> prop.Table2a = prop.table(Table2a)
> prop.Table2a
Liveborn Stillborn
Male 0.5021082 0.01201133
Female 0.4750035 0.01087703


> sum.prop.Table2a = addmargins(prop.Table2a)
> sum.prop.Table2a
Liveborn Stillborn Sum
Male 0.5021082 0.01201133 0.5141195
Female 0.4750035 0.01087703 0.4858805
Sum 0.9771116 0.02288836 1.0000000


>


If A and B are two events, then the probability that both A and B will occur is equal to the probability that A will occur multiplied by the conditional probability that B will occur given that A has occurred, 

P(A and B) = P(A) x P(B|A)

The conditional probability of an event B givent another event A, written P(B|A), is the probability that B will occur if we consider only those occasions on which A also occurs; it is thus the limiting value of the proportion n(A and B) / n(A), where n(A and B) is the number of times on which both A and B have occurred and n(A) is the number of times on which A has occurred.P(B|A) = n(A and B) / n(A)




When the conditional probability of B given A is equal to the unconditional, or absolute, probability of B the two events are said to be "statistically independent".

If A and B are statistically independent, P(B|A) = P(B) and the law of multiplication takes the simple form

P(A and B) = P(A) x P(B)




The Law of Multiplication

The Two Concepts of Probability (Bulmer, 1979)

Statistical probability & Inductive probability


Statistical probability
- It is an empirical concept.
- We can never know with certainty the exact probability of an event.


Inductive probability
- logical concept.



Monday, July 18, 2011

To My Baby-Daughter

Quote from Rocky Balboa:

No matter what happens, you are my daughter and my blood.
You're the best thing in my life.

I love you. - Dad -