SDS321HW24Sol

# SDS321HW24Sol - 1 Blast from the Past a*What is the...

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1. Blast from the Past: a. *What is the probability that I pull a green candy from this bag when I open it and pull out a candy? (prior prediction) For our candy example, let’s assume that the manufacturers advertise a prior over the distribution of bag types of (0.1,0.2,0.4,0.2,0.1). Let d=data (candy observed) and h i for i=1,2,3,4,5 be the type of bag. How did we determine the probability that the first candy selected is green? P(d=Green)=(.1) (0)+ (.2) (.25)+ (.4) (.5)+ (.2) (.75) +(.1) (1) =.5 This is known as the Prior Prediction. b. *What is the probability that I have Bag i , i=1,..5 given I pull a green candy from this bag? *We answered both of these questions the day we investigated the candy bags so this is review. When we want to get information about the type of bag from observations if we observe one green, we found. P(h i |d=Green)=P(h i d= Green)/P(d=Green) P(h 1 |d=Green)=0 P(h 2 |d=Green)=.1 P(h 3 |d=Green)=.4 P(h 4 |d=Green)=.3 P ( d = Green ) = P ( d = Green h i ) = P ( h i ) P ( d = Green | h i ) i i

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P(h 5 |d=Green)=.2
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