Question 1 (11 points). Book Wall Industries supplies bookshelf kits that pair solid wood with iron-pipe supporting structure. We begin by focusing on the wood material required. This depends on the number of bookcases demanded in a month, which is a random variable and denoted X'. An empirical probability model (with 17 possible values of X) defines X. In order to save you the hassle of entering the entire probability model, we make it available in file called BookWall.cov. A graphical display of this probability model is shown in the figure below. Probability Mass 0.00 0.10 200 400 600 800 1000 1400 X (units per month) Figure. A graphical display of the probability model for the number of bookshelves demanded. The number of bookshelves ordered in any one month varies between 100 and 1500 units, as per the probability model that is found in the associated BookWall.cav file. (Be sure to note the units describing your answers whenever pertinent.) a. [1 point] Please determine the expected value for X. b. [2 points] Please determine coefficient of variation for X. Each bookshelf requires 1.2 square-meters of wood. Standard practice involves ordering an additional 80 square-meters per month (regardless of X) as a contingency (spare wood to compensate for mistakes in carpentry). Consider BookWall Industries' monthly wood order (MWO). c. [1 point] Express the random variable MWO as a simple algebraic function of X (the number of desks to be produced) being sure to consider the aforementioned spare-wood. d. Determine the following for the random variable MWO. 1. [2 points] Its expected value ii. [2 points] Its standard deviation e. [1 point] The amount of iron pipe required (linear meters) per month to complete the Bookshelf kits is also a random variable (labeled Y). The expected value and standard deviation are ] and 0.35 (in linear kilometers per month) respectively. Determine the coefficient of variation for Y. f. If the price of wood is 35 dollars per square-meter and the price of pipe is 225 dollars per linear kilometer, determine the following for the total cost of materials (wood and pipe) per month (label this Z). 1 . [1 point] The expected value ii. [2 points] The coefficient of variation