Let X 1 , , X n be an i i d sequence of Uniform (0, 1) random variables Let M max(X 1 , , X n ) (a) Find the density function of M (b) Find E M and V M

Question: Let X 1 , . . . , X n be an i.i.d. sequence of Uniform (0, 1) random variables. Let M = max(X 1

Let X₁, . . . , X_n be an i.i.d. sequence of Uniform (0, 1) random variables. Let M = max(X₁, . . . , X_n).
(a) Find the density function of M.
(b) Find E[M] and V[M].

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