Statistics Assignment Help With Bayes Theorem

2.9 Bayes Theorem:

If E1, E1,………. En are mutually disjoint events with P(Ei) ≠0, (i= 1, 2,…….,n) then for any arbitrary event A which is a subset of bayes theorem such that P(A) >0 we have

theorem of probability , i =1, 2,…n

Proof:

Since mutually disjoint events , we have

compounded-theorem-of-probability

Since bayes theorem (i=1,2…..n) are mutually disjoint events, we have by addition theorem of probability

theorem of probability

By compounded theorem of probability.

Also we have

mutually disjoint events

compounded theorem of probability

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