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Tutorial 4 - ENGM2:032 Applied Probability alid Statistics...

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, ) ENGM2:032 j Applied Probability alid Statistics Winter:2OC 0 TutOrial Problelil,S ;. Assignment 4 1) Suppose that the daily noon-time average temperature. in degJ;ees Celsius. for Pebroary 1 in ' Yarmouth, has the following probability mass function (obtained by rounding to the nearest whole degree andignorlng temperatures with -qeg1igible probabilities); -2 -1 1).10 0.20 2, 3 '0.15 0.05 Find the 'following: a) :i? (X ~ 0]. b) P[...:1<X<2]. c) compute F(z) and sketch its graph. 'd) (;omp~E [X], e) compute Vat [X]. 2) The maximuin poWer that a, particuI~ windm;ill can ~ucej due to IIiechanica1, and e_ectrical CQD.Stralnts. is 4 kW. Suppose that the power 8Ct1Jally demaflded of thiS Windmill at any instant in time is a random variable. X. with·probability density function (pdt) given by ( Jx(z) = {c(4 -,z)2 if 0 ~ z ~ 4kW. o otherwise ' a) If Ix{t&) is a valid pdf, what must the constant cbe? b) What is the expected power .demanded from this windmill? c) What is the stancJard deviation of the power demanded from this windmill? d) What is the probability that the power demanded from this windmill exceeds 3 kW? 3) An Atlantic fish farm produces random amOlmts of cod, Xl> and $8lmon.
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