Transcription of Continuous r.v practice problems - Carnegie Mellon School ...
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Continuous r.v practice problems - Carnegie Mellon School ...
Continuous practice problemsSDS 321 Intro to Probability and Statistics1. (2+2+1+1 = 6 pts) The annual rainfall (in inches) in a certain region is normally dis-tributed with mean 40 and standard deviation 4.(a) What is the probability that, starting with this year, it will take over 10 years beforea year occurs having a rainfall of over 50 inches?LetRdenote the amount of (R 50) =P(R 404 ) = 1 ( ) =.006. LetXbe the number of years before we see over 50 inches of (X 10) =P(None of the first 10 years have more than 50 inches of rain) = (1 .006)10=. pt for gettingP(R 50). 1 pt for correct calculation with geometric.(b) What is the probability that at least 4 out of the next 50 years will have a rainfallof over 50 inches?This is a binomial probability withn= 50,p=.006 andnp=.3. May be better touseX Poisson(3) whereXdenotes number of years with rainfall more than (X 4) = 1 (3 i=0P(X=i)) = 1.
P(X 10) = P(None of the rst 10 years have more than 50 inches of rain) = (1 :006) 10 = :94. 1 pt for getting P(R 50). 1 pt for correct calculation with geometric.
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