I have this problem that i am doing, but i am having a major blank of how to move forward with this question. As it is I have calculated this joint probability table where n=5:
π Prior Y=0 Y=1 Y=2 Y=3 Y=4 Y=5 Posterior 0.30 0.1 0.0168 0.0360 0.0309 0.0132 0.0028 0.0002 0.1131 0.45 0.2 0.0100 0.0412 0.0674 0.0552 0.0226 0.0038 0.2468 0.55 0.3 0.0057 0.0339 0.0828 0.1011 0.0618 0.0150 0.3032 0.60 0.4 0.0040 0.0308 0.0920 0.1384 0.1036 0.0312 0.3369 0.0365 0.1419 0.2731 0.3079 0.1908 0.0502
And also this table with the calculation for the posterior probabilities given that we have observed y=2:
π Prior Likelihood Prior*Likelihood Posterior 0.30 0.1 0.309 0.0309 0.1131 0.45 0.2 0.337 0.0674 0.2468 0.55 0.3 0.276 0.0828 0.3032 0.60 0.4 0.230 0.0920 0.3369 0.2731
It has then stated that- the likelihood is proportional to π^y.(1-π)^n-y where n=5 and y=2. Redo the calculations using that likelihood.
π Prior Likelihood Prior*Likelihood Posterior 0.30 0.45 0.55 0.60
Any help with how to go about this would be greatly appreciated