sp07ex4asol - STA 4321/5325 Spring 2007 Exam 4 6th period...

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STA 4321/5325 – Spring 2007 – Exam 4 – 6 th period PRINT Name Legibly __________________________________ The following table gives the joint probability distribution for the numbers of washers (X 1 ) and dryers (X 2 ) sold by an appliance store salesperson in a day. Washers\Dryers x2=0 x2=1 x2=2 x1=0 0.25 0.08 0.05 x1=1 0.12 0.20 0.10 x1=2 0.03 0.07 0.10 Give the marginal distributions of numbers of washers and dryers sold per day. Give the Expected numbers of Washers and Dryers sold in a day. w\d 0 1 2 f(w) w*f(w) E(W) 0 0.25 0.08 0.05 0.38 0 0.82 1 0.12 0.2 0.1 0.42 0.42 2 0.03 0.07 0.1 0.2 0.4 f(d) 0.4 0.35 0.25 d*f(d) 0 0.35 0.5 E(D) 0.85 Give the covariance between the number of washers and dryers sold per day. wdf(w,d) 0 1 2 0 0 0 0 1 0 0.2 0.2 2 0 0.14 0.4 E(WD) 0.94 COV(W,D) = 0.94-(0.82*0.85) = 0.243 If the salesperson makes a commission of $100 per washer and $75 per dryer, give the average daily commission. E[C] = E[100W+75D] = 100*(0.82) +75*(0.85) = $147.75
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The number of stops (X 1 ) in a day for a delivery truck driver is Poisson with mean λ . Conditional on their being X
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sp07ex4asol - STA 4321/5325 Spring 2007 Exam 4 6th period...

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