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Homework 3 Solutions _

# Homework 3 Solutions _ - Homework 3 Solutions Note...

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Homework 3 Solutions Note: Solutions are incomplete if the solution to the first part is a good representation of the solutions to the other parts. 3.75 a. ( 29 ( 29 ( 29 ( ) ( ) ( | ) ( ) | .3(.4) .8(.6) .12 .48 .6 P A P A B P A B P A B P B P A B P B = + = + = + = + = I I b. ( ) ( | ) ( ) .3(.4) ( | ) .2 ( ) ( ) .6 P B A P A B P B P B A P A P A = = = = I c. ( 29 ( 29 ( 29 .7(.4) .28 | .7 .7(.4) .2(.6) .4 P B A P B A P A = = = = + I 3.78 V and W consider bidding. V will definitely put in a bid, and 3 4 ( | ) P Vgets Wnotbid = 3 4 1 3 ( ) ( | ) P Wbid P Vgets Wbid = = a. P(V gets job) = ¾*1/3+1/4*3/4=.4375 b. P(W did not bid | V gets job) = P(W did not bid and V gets job) / P(V gets job) =1/4*3/4 / .437=.4286

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4.3 a. All values ≥0 and add to exactly 1, so this is a probability distribution. b. The values add to >1, so this can’t be a probability distribution. c. Not all values ≥0, so this is not a probability distribution. 4.4 a. not add to 1; b. For x=2, the probability will be negative, so this is not a probability distribution; c. All values ≥0 and they add to 1, so this is a probability distribution.
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