You are the zookeeper and it is midnight at the zoo. The lights have gone out an

Question

You are the zookeeper and it is midnight at the zoo. The lights have gone out and it's pitch black. You hear an animal rustling in the bush behind you. There are exactly 10 animals in the zoo Aardvark, Bear, Cougar. Deer. Elephant, Fox, Giraffe, Hippo. Iguana, and Jackal You know one of them is behind that bush, but you don't know which one. Your byupothesis set consists of ten hypotheses, each corresponding to one animal. You set your hypothesis is equally probable fie, each has a prior probability of Q.10. prior probabilities so that each At 12:01am, you hear the animal make a exhaustive knowledge of animal sounds, you know the animal hypothesis: behind the bush make a "ring-ding-ding" sound. Because you have following kellhoods associated with each 0.30 0.20 0.20 0.10 0.10 0.90 0.10 0.20 0.30 0.10 Bear Came Elephant Fox Giraffe Hippo Using Bayes' Rule, what is your posterior probability for each of the ten hypotheses? NOTE: Please report all your answers as probabilities (not percents) and round all answers to 2 decimal places. What is the posterior probability for Aardvark? What is the posterior probability for Bear? What is the posterior probability for Camel? What is the posterior probability for Deer? What is the posterior probability for Elephant? What is the posterior probability for Fox? What is the posterior probability for Giraffe? What is the posterior probability for Hippo? What is the posterior probability for Iguana? What is the posterior probability for Jackal?

Explanation / Answer

According to bayes rule we know Posterior probability = Prior probability x conditional probability

ANIMAL PRIOR PROBABILITY SOUND GIVEN HYPOTHESIS POSTERIOR PROBABILITY Aardvark 0.10 0.30 0.03 Bear 0.10 0.20 0.02 Camel 0.10 0.20 0.02 Deer 0.10 0.10 0.01 Elephant 0.10 0.10 0.01 Fox 0.10 0.90 0.09 Giraffe 0.10 0.10 0.01 Hippo 0.10 0.20 0.02 Laguana 0.10 0.30 0.03 Jackal 0.10 0.10 0.01

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