Please help:
Restaurant open for dinner and lunch You own a restaurant. It's open for lunch and dinner (and closed in between). Net revenue during dinner (X) ranges from 100 to 400. Net revenue during lunch (Y) ranges from 100 to 300. X and Y are independent and jointly distributed uniform random variables. 9. In the graph of the probability density function below, what is the value of \"a\"? Integer 10. Continued. What is the value of "b\"? Integer 11. Continued. What is the value of "c\"? Integer 12. Continued. What is the value of \"d\"? Integer 13. 14. 15. 16. Continued. In the graph, "height\" equals 1/denominator. What is the value of \"denominator\"? Integer What is the probability that net revenue will be leithan 200 for both lunch and dinner, on a given day? Four decimals HINT: In the graph of the pdf (above), identify the area on the "floor\" where net revenue is less than 200 for lunch and net revenue is less than 200 for dinner. Calculate that area. Then multiply by the \"height\" of the pdf to obtain the relevant volume under the pdf. (This is analogous to the process of multiplying "height\" times "width" to obtain a probability, for % uniformly distributed random variable.) Alternatively, you can write down and evaluate an expression (double integral) for the volume. What is the probability that net revenue will exceed 200 for both lunch and dinner, on a given day? Four decimals HINT: This event and the event in the previous question are not complements. Approach this question the same way as you approached the previous question. What is expected total net revenue per day? (Here we're asking about revenue for the day. Here it doesn't matter whether a dollar of net revenue comes in at lunch or dinner.) Two decimals 17. 18. You need 300 per day to pay your workers and 100 per day for other operating costs. Therefore, you ca re about the probability that (on any given day), total net revenue will be at least 400 (to help you manage cash flow). What is this probability? Four decimals HINT: You need to calculate the area on the \"floor\" of the pdf where total net revenue is at least 400. Sketch the floor of the pdf (represent the X,Y plane, and mark the set of possible pairs of values ofX and Y using your values of a, b, c, and d). Graph a line along which total revenue equals 400. The line segment where this line intersects the set of possible pairs of values of X and Y is the line segment you care about. Figure out on which side of this line segment total revenue exceeds 400. Now you have the area on the \"floor" of the pdf where total net revenue is at least 400. Calculate this area using a rectangle and a triangle. Finally, multiply the area by the height of the pdf to obtain the volume that is the probability you want to find. As owner, you keep all profit (profit is total net revenue minus 400 for wages and other operating costs). What is expected profit per day? Two decimals
