Dear all,
I am a little bit confused on how is the p(X|Y=1)=>(1/2,1/4,1/8,1/8) are being generated which originally in the figure shown as =>(1/8:1/4,1/16:1/4,1/32:1/4;1/32:1/4)?
I'm eager to hear any prompt respond from anyone here & cheers.
It is simple
Sum(p(X|Y=1) must be 1and the ratio is by p(X,Y=1) thus p(X|Y) = k p(X,Y), where k is a constant. To satisfy Sum(p(X|Y=1) in this case k=1/4.
Dear saso tomazic , many thanks for the explanation. For second confirmation, we can only satisfy with the k value 1/4 due to all the sequence elements within that ratio 1/4. Otherwise, if in any element say 1/15, we shall remains that original values isn't it?
Generaly it holds:
p(X,Y)=p(Y) p(X/Y)
thus
p(X/Y)=P(X,Y)/P(Y)
In your case p(X,Y) is given in the table (e.g. 1/8, 1/16, 1/32,1/32) and P(Y)=1/4
thus
P(X/Y)=4 . (1/8, 1/16, 1/32, 1/32) = 1/2,1/4,1/8,1/8)
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