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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- May 4th 2010, 02:59 PMAdelphiProbability - random variables
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))?

- May 4th 2010, 04:09 PMmatheagle
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. - May 4th 2010, 07:32 PMAdelphiThanks
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))?

- May 4th 2010, 08:26 PMmatheagle
OH, now you give the necessary info

with iid then you know the joint density