Question

Question 2. (3 marks) The cost of fuel fluctuates due to many factors. Suppose that, on any given day, the fuel price at a specific retailer consists of: • A fixed government fuel excise of $0.416 per litre. • Wholesale supplier costs, which average $0.712 per litre, with a variance of 0.10. • Retail costs, including a profit margin, which average $0.212 per litre, with a variance of 0.0012 (a) Find the average total fuel price on any given day. (b) Given that wholesale supplier costs and retail costs have a correlation of 0.7, find the vari- ance of the total fuel price. (c) Assuming that the total fuel price is normally distributed, what is the probability of fuel being priced at less than $1 per litre on any given day?

Answer 1

$0.416 Hz --- Bio Flaced govt. esuje : a = X; : Wholesale Supplier verdt XANN(0.712, 0:10) Xr: Retail cost - X N1 0: 21t, 6 •012) ext: Y: Total pure of full on ony givendey ELY]: Ela + xy + x2] = Q t E(X1) + E(&) 2 0.712 + 0.416 + 0-212 31-34 V[y] = [atx, & XzJ = v(x) + V (X₂) -2 lov(x, xd 01 +0.0012 - conlX, X₂), care .(x, y) =aat Sucx, ) V (X2) .:CON (XX.)67 x Juca) vs) < 0.007668 i vy) =_0 10012 - 0:00266) = 0.09245 Yo NC 134, 0.09245) PL 4<1] = $ 1134 = 4(1-1.34 ) 07-1:1182) = 0-1317 Read Jo.04240