Supose you have 3 RV X1, X2 and X3. You know the CDF of each of them. How to find the P(x1>max(x2,x3))?
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you need the joint distribution in order to determine
the probability that X1 is the largest
And you'd just integrate or sum over that region.
Thank you for your help. My problem has 3 iid normal RV with the following parameters: X1~N(0.40,0.22), X2~N(0.47,0.08) and X3~N(0.60,0.13). How can I build the joint pdf and calculate P(x1>max(x2,x3))?
OH, now you give the necessary info
with iid then you know the joint density
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