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P0082_Soln

# P0082_Soln - EX = np 2.06 = 7(29 p p =.29 This parameter p...

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P0082_Soln.doc Days 0 1 2 3 4 5 6 7 prob 0.0 8 0.2 6 0.3 2 0.2 2 0.1 0 0.0 2 0 0 This marginal PMF shows us the probability of having a headache on k many days in week. We can view this as a binomial PMF by thinking of this as telling us the probability that we will have k successes (days with headache) in n attempts (days). Observed mean from this PMF was EX [] = xp X x ( 29 x = 0 ( 29 0 .08 ( 29 + L + 7 ( 29 0 ( 29 = 2 .06 In other words, on average we expect to have a headache 2 days per week. Mean of binomial RV is EX [] = np We know that n = 7 since every day of the week we “attempt to have a headache”
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Unformatted text preview: EX = np 2 .06 = 7 (29 p p = .29 This parameter p can be interpreted as the probability of having a headache on any given day. Can check this by computing the probabilities for binomial RV using p X k (29 = n k p k 1-p ( 29 n-k >> % in MATLAB >> binopdf([0 1 2 3 4 5 6 7], 7, 0.29) ans = Columns 1 through 5 0.09 0.26 0.32 0.22 0.09 Columns 6 through 8 0.02 0.00 0.00 ANSWER: B...
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