rv.7.3b.2010W.ST.12B.L10X

rv.7.3b.2010W.ST.12B.L10X - 2 0.2 0.1 0.3 3. Probability (1...

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Description Problem 7.3b Y's and 0 1 2 X's 0 0.1 0.1 0 0.2 1 0.1 0.2 0.2 0.5 2 0 0.2 0.1 0.3 0.2 0.5 0.3 A farm equipment dealer has obtained the joint probabilities of selling X tractors on day 1 and Y tractors on day 2. The findings are summarized below. (I) Find the marginal distributions. (ii) Are the two random variables independent? (iii) Find the average number of tractors sold on day 1. Find the variance of the number of tractors on day 2. (iv) Find the distribution of the sales on two successive days. Calculate the expectation and the variance of this distribution. Additional Question: (v) Suppose that each tractor sold has a selling price of \$35,000 and a cost of \$20,000. Also assume that daily overhead costs are \$3,000 per day. Determine the average profit over the two day period.Determine the standard deviation of profit over the two day period.

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Probability.Questions What is: Y's 1. Probability(no sales on day 1 and day 2) Joint 0 1 2 X's 0 0.1 0.1 0 0.2 2. Probability( that sales on day 1 is at least 1) 1 0.1 0.2 0.2 0.5

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Unformatted text preview: 2 0.2 0.1 0.3 3. Probability (1 sale on Day 1 or 2 sales on Day2) 4. Given that there is 1 sale on Day 1, what is the probability that there will be at least 1 sale on Day 2? Prob Answers Answers (Calculations) 1. P(x=0 and Y=0) 0.1 2. P( X>= 1) 0.8 (.5+.3) 3. P( X=1 or Y=2) 0.6 (.5 +.3 - .2) 4. P(Y>=1 | X = 1) 0.8 (.2+.2)/.5 Additional Answers Solution Day1 Profit = Revenue - Costs = 35X - (20X + 3) = 15X -3 and Day 2 Profit = Revenue - Costs = 35Y - (20Y + 3) = 15Y -3 Total Profit Day 1 & 2 = 15X -3 + 15Y -3 = 15X + 15Y - 6 Want E(Profit Day 1& 2) = E(15X + 15Y - 6 ) = E(15X) + E(15Y) - 6 = 15E((X) + 15E(Y) - 6 = 15(1.1) +15(1.1) - 6 = 27 So, expected profit from day 1 and 2 sales is \$27,000 Additional Question: (v) Suppose that each tractor sold has a selling price of \$35,000 and a cost of \$20,000. Also assume that daily overhead costs are \$3,000 per day. Determine the average profit over the two day period....
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This note was uploaded on 01/03/2011 for the course COMM 290 taught by Professor Brian during the Winter '09 term at The University of British Columbia.

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rv.7.3b.2010W.ST.12B.L10X - 2 0.2 0.1 0.3 3. Probability (1...

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