Let X 1 , X 2 ,...,X n be independent random variables, all with a U(0, 1) distribution. Let Z = max{X 1 ,...,X n } and V = min{X 1 ,...,X n }. a. Compute E[max{X 1 , X 2 }] and E[min{X 1 , X 2 }]. b....

Let X₁, X₂,...,X_n
be independent random variables, all with a U(0, 1) distribution. Let Z = max{X₁,...,X_n} and V = min{X₁,...,X_n}.

a. Compute E[max{X₁, X₂}] and E[min{X₁, X₂}].

b. Compute E[Z] and E[V ] for general n.

 c. Can you argue directly (using the symmetry of the uniform distribution (see Exercise 6.3) and not the result of the computation in b) that