Distribution function of a maximum

Topic: Joint distributions · more questions on this topic
‹ A probability as an integral One weight, or six weights ›

Let X_1,\ldots,X_n be independent with distribution functions F_1,\ldots,F_n. Express the distribution function of M=\max(X_1,\ldots,X_n) in terms of F_1,\ldots,F_n.

Worked answer (click to show)

The maximum is at most m when every variable is at most m. Independence factors the probability:

\mathbb{P}(M\le m)=F_1(m)\cdots F_n(m).