3. Based on years of a mild caffeine addiction and a very keen sense of observation, your professor has determined the probability distribution function of x, the number cars in the drive-through line at 8:00 am to be as follows: ______I-_ (a) Sketch the probability density function for X (2 marks) (b) Find the probability that on a given day more than 3 cars will be in line (2 marks) (c) Compute the expected value of the random variable X. Interpret this result. (3 marks) (d) Compute the variance and standard deviation of X (2 marks each) 6. Given the following observations (x,y): (3,5); (2,2); (1,3); (-1,2); and (0,-3), find the following by hand (no calculator permitted - show all of your work) (15 marks): a) Ex? , Extyt, Ext , Eye, x, y (1 mark each) b) b, and b2 (2 marks each) c) Graph y = b1 + b2xt (2 marks) d) Interpret the meaning of b, and b2 (1 mark each) e) Suppose that you know the value of the intercept is zero ( B, = 0). Derive the new equation for b2. (Hint as aB = -2 Extyt + 2p Ex? ) (4 marks) f) Using your answer from part e) calculate b2 using the (x,y) pairs above (2 marks)