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[Steps Shown] Let X_1,X_2,....,X_n be independent random variables, and all are U(0,1). Define X=max X_1,...,X_n V=min X_1,X_2,...,X_n Compute E(max X_1,X_2)

Question: Let ${{X}_{1}},{{X}_{2}},....,{{X}_{n}}$ be independent random variables, and all are $U\left( 0,1 \right)$. Define

\[X=\max \left\{ {{X}_{1}},...,{{X}_{n}} \right\}\] \[V=\min \left\{ {{X}_{1}},{{X}_{2}},...,{{X}_{n}} \right\}\]

Compute $E\left( \max \left\{ {{X}_{1}},{{X}_{2}} \right\} \right)$ and $E\left( \min \left\{ {{X}_{1}},{{X}_{2}} \right\} \right)$
Compute $E\left( X \right)$ and $E\left( V \right)$ in general.
Can you argue directly that $1-E\left( \max \left\{ {{X}_{1}},...,{{X}_{n}} \right\} \right)=E\left( \min \left\{ {{X}_{1}},...,{{X}_{n}} \right\} \right)$

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[Steps Shown] Let X_1,X_2,....,X_n be independent random variables, and all are U(0,1). Define X=max X_1,...,X_n V=min X_1,X_2,...,X_n Compute E(max X_1,X_2)

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