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Assignment IV - ENGM2032 Applied Probability and Statistics...

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ENGM2032, Applied Probability and Statistics Winter 2010 Assignment #4 Due: Tue Feb 7, 2010 1) Four cards are dealt from a shuffled deck of 52 cards. Let X count the number of spades appearing in the four dealt cards. a) What is the probability mass function for X ? b) What is the expected value of X ? 2) A company has determined that the drilling depth X , in metres, before encountering oil in a certain region is random and distributed according to f X ( x ) = 0 . 002 e - 0 . 002 x for x 0 a) What is the probability that the next well drilled will encounter oil at a depth exceeding 700 m? b) Out of the next 7 wells drilled, what is the probability that exactly three of them exceed 700 m in depth before striking oil? 3) Suppose that by rounding the records, the following discrete probability mass function has been determined for the average temperature, T in o C, in Halifax over the month of March: t -6 -4 -2 0 2 4 P T = t 0.10 0.10 0.30 0.25 0.15 0.10 Find the following; a) P T 0 , b) P 4 < T < 4 , c) compute F T ( t ) and sketch its graph, d) compute E T , e) compute Var T .
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  • Spring '10
  • yao
  • Probability distribution, Probability theory, probability density function, Cumulative distribution function, Probability mass function

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