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IAI october 2009

P

Parvathi Reddy

Member
In question 9, how is the pdf of U calculated?-why are we considering 1-P(x>u) and in case of V, P(x<=v)?
 
In the case of U = min {X1, ....Xn}, then F(u) = P(U<=u) is the probability that the smallest value is less than or equal to u. We can't work out this directly because the smallest one might be less than u but what values do the others take? However, we can say that F(u) = P(U<=u)=1-P(U>u). If the minimum value is greater than u, then all the values must be greater than u, so P(U>u) is [P(Xi>u)]^n.

The same argument then applies to V.
 
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