SampleMidtermSolutions

# SampleMidtermSolutions - MIDTERM EXAM(Form A PSTAT 5E HSU...

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PSTAT 5E HSU 4/30/2010 Fully explain your answer. Answers with no explaination will not receive credit. GOOD LUCK!!! 1. (40%) I have two cats, Ray and Felix, who behave independently of one another. I know that at 4:00 pm there is a 0.3 chance that Ray will be in my garage and 0.9 chance that Felix will be in my garage. (a) (10%) If I walk into my garage some day at 4:00 pm, what is the probability that both cats will be in the garage? 0 . 3 × 0 . 9 = 0 . 27 (b) (10%) If I walk into my garage some day at 4:00 pm, what is the probability that at most one cat will be there? 1 - 0 . 27 = 0 . 73 (c) (10%) Consider the random variable X which represents the number of cats I ﬁnd in my garage at 4:00 pm. Find the probability distribution of X. f (0) = 0 . 7 × 0 . 1 = 0 . 07, f (1) = 1 - 0 . 07 - 0 . 27 = 0 . 66, f (2) = 0 . 27 (d) (10%) Calculate the expected value and variance of X in (c). E

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SampleMidtermSolutions - MIDTERM EXAM(Form A PSTAT 5E HSU...

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