Q5 A student wrote a (machine learning) algorithm for distinguishing.pdf

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Q5 A student wrote a (machine learning) algorithm for distinguishing between pictures of cats and pictures of dogs. The error rates of her algorithm are given as: P(alg=dogpic=cat)=0.1P(alg=catpic=dog)=0.2. [For example, P(alg= cat pic=dog) denotes the probability that the algorithm outputs "cat" when seeing a picture of a dog.] Now we test the algorithm for several rounds, each round inputting to it a random picture of either a cat or a dog. For each picture, the probability of it being a cat's picture is 0.3 and the probability of it being a dog's picture is 0.7 . a) What is the probability that the algorithm correctly classifies 3 consecutive pictures? (5 points) b) When the algorithm outputs "cat", what is the probability that the picture actually shows a cat? (5 points) c) Suppose we run this test for 5 rounds, and we award the student 10 HKD for each picture that her algorithm correctly classifies (and 0 HKD for each wrong classification). What is the variance of her income? (5 points).

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