) Let U1, , Un be i.i.d. Unif(0, 1), and X = max(Ui, , U.). What is the PDF of X? What is EX? Hint: Find the CDF of X first, by translating the event X

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Answered Same DayDec 26, 2021

Answer To: ) Let U1, , Un be i.i.d. Unif(0, 1), and X = max(Ui, , U.). What is the PDF of X? What is EX? Hint:...

Robert answered on Dec 26 2021

123 Votes

The distribution of the order statistics is given by:
( )

( ) ( )
, ( )- , ( )- ( )
( ) *
+
a)
( )

( )
b)
E(X) = ∫ ( )

∫

( )
( )
∫
, -
hence, E(X) =

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) Let U1, , Un be i.i.d. Unif(0, 1), and X = max(Ui, , U.). What is the PDF of X? What is EX? Hint: Find the CDF of X first, by translating the event X

Answer To: ) Let U1, , Un be i.i.d. Unif(0, 1), and X = max(Ui, , U.). What is the PDF of X? What is EX? Hint:...

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