1) The following table lists the joint probability distribution between recipients of the Nobel prize in...

 

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1) The following table lists the joint probability distribution between recipients of the Nobel prize in economics and the other five prizes, and the citizenship of the recipients, based on the 1969-2001 period. Economic Nobel prize (X=0) Physics, Chemistry, Medicine, Literature, and Peace Nobel prize (X= 1) Total U.S. citizen Non-U.S. citizen Total (Y=0) (Y= 1) 0.118 0.019 0.345 0.488 0.463 0.537 0.167 0.833 1.00 a) Compute E(Y) and E(Y|X=0) and interpret the resulting numbers. b) A randomly selected Nobel Prize winner reports that he is a non-U.S. citizen. What is the probability that he has won the Nobel Prize in any field other than Economics. Use Bayes' rule. c) Show what the joint distribution would look like if the two categories were independent. Verify that now E(Y)=E(Y|X=0). 1) The following table lists the joint probability distribution between recipients of the Nobel prize in economics and the other five prizes, and the citizenship of the recipients, based on the 1969-2001 period. Economic Nobel prize (X=0) Physics, Chemistry, Medicine, Literature, and Peace Nobel prize (X= 1) Total U.S. citizen Non-U.S. citizen Total (Y=0) (Y= 1) 0.118 0.019 0.345 0.488 0.463 0.537 0.167 0.833 1.00 a) Compute E(Y) and E(Y|X=0) and interpret the resulting numbers. b) A randomly selected Nobel Prize winner reports that he is a non-U.S. citizen. What is the probability that he has won the Nobel Prize in any field other than Economics. Use Bayes' rule. c) Show what the joint distribution would look like if the two categories were independent. Verify that now E(Y)=E(Y|X=0).

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