Unformatted text preview: Find the numerical value o± E [ g ( X )] and var( g ∗ ( X ))? (c) Find the mean square error E [( Y − g ∗ ( X )) 2 ]. Is that the same as E [var( Y  X )]? (d) Find var( Y ). 3. Random variable X is uni±ormly distributed between 1.0 and 1.0. Let X 1 , X 2 , . . . , be independent identically distributed random variables with the same distribution as X . Determine which, i± any, o± the ±ollowing sequences (all with i = 1 , 2 , . . . ) are convergent in probability. Give reasons ±or your answers. Include the limits i± they exist. (a) X i X i (b) Y i = i (c) Z i = ( X i ) i (d) T i = X 1 + X 2 + . . . + X i X 1 + X 2 + . . . + X i (e) U i = i (±) V i = X 1 · X 2 · . . . · X i (g) W i = max( X 1 , . . . , X i ) Page 1 o± 2...
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This note was uploaded on 12/08/2010 for the course MATH 6.041 / 6. taught by Professor Muntherdahleh during the Spring '10 term at MIT.
 Spring '10
 MuntherDahleh
 Systems Analysis, Probability

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