ee302hw3_Fa09

ee302hw3_Fa09 - ECE302 Homework #3 Assigned 9/21/09, Due...

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i iij i ±∞ || ±∞ ±| | ² ±∞ ±∞ ±² R ³ ³ ³ ³ ³ ³ RR 3 +1 3 1 2 :( )= :() =1 2 ECE302 Homework #3 X Xi x i X x Y Y Yj xgx yXi Y d dy xgx y X Y n i dx dy i YX = ( ) = 2exp( 2 ) 0 =0 2 ()= 1 2 =01 2 = =() = 1 =2 ? () E [] ( )= ( ) ( =() = 1 = ( ) () = () () E [+ ] = E []+ Var[ + ] = Var[ ] Var[ ] = 0 = 0 Y X . X fx x , < x <. , Y, Y X. X p x , x , ,. .., , YY X . Yg X a b. e, < x < Y fy Y XY g X . p y p x . g X . f y f x d x g X . f y f x y g x ,i ,. ..,n. X Y g X . yf y dy g x f x dx Xa b a X b a X b b a X b a X XX X . Assigned 9/21/09, Due 10/2/09 (by 4:30 in dropbox in MSEE 330) 1. Text, problem 4.77, page 222 2. A random variable is related to a random variable by (a) Suppose is a continuous random variable with pdf else Find the pdf of and the probability that is greater than (b) Suppose is a discrete random variable with pmf else. Find the pmf of and the probability that is greater than (c) Explain how the answers to the above two parts change if 3. Consider the limiter shown in Figure P4.3 on p. 220 of the text with and . Assume that (a) What kind of random variable is (b) Find using the density method (c) Find using the distribution method
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