Problem 4 [37 points (7, 7, 7, 6, 6, 4)]: Bike Shop Expected Value Variance The table below gives the probability of invoices2 customers receive when they walk into a bikeshop. Note that every bill has both a (M)aterials and (Ljabor cost associated with the repair. Repair Just Looking Flat (tube replaced) New Tube 85 Tire Drivetrain overhaul 2\"invoicu\" aren't really given to customer's for just looking, but including them in our model is helpful as it allows us to connect foot-trafc in the store to billing Let M , L be the random variables indicating the materials and labor costs of a customer's bill respectively. i Compute E[M]. Give one sentence which explains the meaning of your computation in the context of the bike shop. ii Compute Var(M) and the standard deviation of M Give one sentence which describes what these values represent. iii To help keep up with ination, the shop decides to increase all materials costs by a dollar. (This includes costs for \"just looking\") How does the new variance of materials, Var(M + 1) compare to Var(M)? Support your answer by explicitly computing and with one clear sentence which summarizes your response. iv Compute the expected value of the total amount (materials and labor) invoiced to 100 customers who walk into the store. v Compute the variance of the total amount (materials and labor) invoiced to 100 customers who walk into the store. vi What is the expected value of the total materials invoice for 20 customers and the total labor cost of another 30 customers