Could you inform me please, how can I calculate conditioned probability of several events?
I have 3 events A, B, C; I know P(B|C) and I want calculate P(A|B,C). Is it possible?
In the special case B,C~Pois(2) and A~Pois(0.3*2) is a splitting of B. I would find P( A(10)=2 | B(10)= 5, C(3)=2 ). I can't find any formula that could help me. Thanks in advance.
Given a Poisson process, I know that P(N(s) | N(t)=n) with s Binomial(n, s/t). Is it also true when I have 2 different PP? In this case the solution could be found as follow:
p=0.3, λ=2 ; A(t)~PP(pλt) B(t)~PP(λ*t).
P( A(10)=2 | B(10)=5, B(3)=2 ) = P( A(10)=2, B(10)=5, B(3)=2 ) / P( B(10)=5, B(3)=2 )= P( A(10)=2 ) * P( B(10)=5 | A(10)=2 ) * P( B(3)=2 | A(10)=2, B(10)=5 ) / P( B(10)=5, B(3)=2 )
I can calculate P( A(10)=2 ), P( B(10)=5, B(3)=2 ). But what about P( B(10)=5 | A(10)=2 ) and P( B(3)=2 | A(10)=2, B(10)=5 ) ?