2. Consider a uniform distribution u[0,1] (meaning minimum value is 0 and maximum is 1) a) Draw this distribution and describe its general shape (5 points) b) What is the probability of a randomly selected value being greater than or equal to a value xi? (5 points) 3. There are two common equations for the variance of a random variable x: 02 = =121=1(xi-x)2 (1) 02 = E[x3] - (6[x])2 (2) a) If (1) refers to a sample. What value of n would make (1) exactly equivalent to (2)? (5 points) b) Assume the criteria from part (a) holds, demonstrate that (1) and (2) are equivalent. Verbal explanations without the mathematical demonstration will receive partial credit. (15 points) 4. Arrivals at a car wash occur once every 10 minutes on average. If a single employee can wash 2 cars per hour, how many employees are necessary for it to be at least 84% likely that there will not be a backlog of customers within a single hour? (15 points)