In Gallup's Annual Consumption Habits Poll, telephone interviews were conducted for a random sample for 1014 adults aged 18 and over. One of the questions was , "How many cups of coffee, if any, do you drink on average day?". The following table shows the results obtained (Gallup website, August 6, 2012). Define a random variable X = number of cups of coffee consumed Number of Cups per Day Number of Responses 0 365 1 264 2 193 3 91 4 or more 101 on an average day. Let X = 4 represent four or more cups. (a) (5 points) Develop a probability distribution for X. (b) (2 points) Compute the expected value of X (c) (2 points) Compute the variance of X (d) (3 points) Suppose we are only interested in adults who drink at least one cup of coffee on an average day. For this group, let y = the number of cups of coffee consumed on an average day. Compute the expected value of y and compare it to the expected value of X