1. [10 points) Taylor's tool life formula for a certain metal is given by XT2=c 1' where X is the cutting speed, T is the tool life in minutes and c is the tool life constant. Notice that X and T are random variables, whereas c is a constant. A sensor is used to measure the cutting speeds when the tool is operationai. It is observed that the cutting speed X is a continuous random variable with PDF i\" nugxgc {} otherwise. The average cost per year ,9 is given by the relation p=, where H is a constant, and i is the average (or mean) life of a tool [in minutes). Therefore, I = E[T]. For a tool with 9 = 2E] and c = 256, calculate p, i.e. the expected [or average} cost per year