Question

3) A metal fabricating plant currently has 5 major pieces under contract, each with a deadline for completion. Let X denotes the number of pieces completed by their deadlines. Suppose that X is a random variable with the probability mass function f(x) given by 10 1 4 2 0.15 3 0.25 f(x) (a) Compute the expected value and variance of X. (4 marks) (b) The plant receives a fixed revenue of $70,000, plus for each piece completed by the deadline.it receives a bonus of $15,000. Find the expected value and variance of the total revenue amount. (4 marks)

Answer 1

Elx) = PCX=se) E 2=0 - Ixo.1 +2 xo.15 +3XD. 25+ 4XD.35 + 5 xool 3.05 VEX) = Elx²) = E(X2) - (E(x))? Ex² pix=x) (1) xool + 2?x0.15 +3²x0,75 + 4X0.35 + 5*X0.), 11.05 = VIX) = 11.05 - (3.05) 107475. x =0 .5. R = 70,ooot 15ooo x. 70,000 & 15,000 Elx). ECR)= - = 70,000 + 15,000 X 3.05 115,750 [v (70,000) = 0 v(R) = (15000) vex) = 115,000) 2x 107415 = 393187500