HW8_sol

HW8_sol - CSE21 FA11 Homework#8 8.1 Solution Draw the...

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CSE21 FA11 Homework #8 (11/17/11) 8.1 Solution. Draw the decision tree. Then compute: (a) Pr ( M 2 = red ) = r r + b + c r r + b + r + d r + b + d b r + b . (b) Pr ( M 2 = red | M 1 = red ) = r r + b + c . Pr ( M 1 = blue | M 2 = blue ) = b r + b b r + d + b r r + d b + c r + b + c + b r + b b r + d + b 8.2 Solution. Let X i be a random variable such that X i = 1 if and only if F i is a head otherwise X i = 0. Thus, we have Pr ( X i = 1) = 2 / 3 and Pr ( X i = 0) = 1 / 3. Note that X = n i =1 X i and X i ’s are independent. We have E ( X ) = E ( n X i =1 X i ) = n X i =1 E ( X i ) = n (2 / 3) = 2 n/ 3 and V ar ( X ) = n X i =1 V ar ( X i ) = n ( E ( X 2 i ) - E ( X i ) 2 )) = n (2 / 3 - 4 / 9) = 2 n/ 9 . 8.3 Solution. Again, draw the decision tree. Then compute: (a) Pr ( G is good ) = 1 - α. 1
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(b) Pr ( T says G is good | G is good ) = γ. (c) Pr ( G is good | T says G is bad ) = Pr ( G is good, T says G is bad ) Pr ( T says G is bad ) = (1 - γ )(1 - α ) βα + (1 - γ )(1 - α ) . 8.4
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HW8_sol - CSE21 FA11 Homework#8 8.1 Solution Draw the...

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