00:01
In this question we have to find the smallest set of independence or conditional independence relationship for the given following problems.
00:10
So the first that we have given to us is probability a intersection b is equal to probability of event a given that b is already occurred multiplied with probability of b.
00:26
So here probability of a given that b is already occurred denotes occurrence of a when b is already occurred.
00:52
So it implies a depends on b.
01:03
So here b is the independent set because a is a is.
01:09
Is dependent on the b.
01:11
So the smallest set of independence for this question is b is the independent set.
01:25
So this is answer to the sub question 1.
01:29
Now in second question we have given probability of a intersection b is equals to probability of a multiplied with probability of b.
01:42
So this we can write when a and b both are independent.
01:57
So here if a is independent of b then probability of event a given that b is already occurred is equal to probability of a.
02:18
So probability of a is equal to probability of a times probability of b.
02:27
Now if similarly b is independent of a, then we have probability of event b given that a is already occurred as equal to probability of b.
02:48
So from these two cases we can observe that the independent set the independent set for this is a comma b.
03:07
So this is answer to the second sub part...