Joint and conditional probabilities



Hi!

if I have genotype on individuals with the following pedigree

c (father) d (mother)
| |
-----------------
|
a offspring 1
b offspring 1

I can write joint probability of genotypes as

P(a,b,c,d)=P(a,b|c,d)P(c)P(d)

But I can write a bit further since a and b are conditionally
independent given c and d i.e.

P(a,b,c,d)=P(a|c,d)P(b|c,d)P(c)P(d)

Is this mathematically OK? i.e. is P(a,b|c,d)=P(a|c,d)P(b|c,d)?

Thanks!

Gregor

.



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