Tutorial 4 - , ) ENGM2:032 Applied Probability alid...

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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. X 2 both measured in kg. each year. It costs $2 per kg to ship the fish to market. At the marlcet. the cod fetches a price of $S/kg and the salmon a price of $8Ikg. If the mean annual yields of cod and salmon are 1200 and 600 kg with coefficients of variation of 0.2 and 0.3, respectively, and the annual mounts of cod and salmon are correlated With correlation coefficient 0.6, then what is the
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This note was uploaded on 02/24/2010 for the course ENGM 2032 taught by Professor Yao during the Spring '10 term at Dalhousie.

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Tutorial 4 - , ) ENGM2:032 Applied Probability alid...

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