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Car Dealership Steve and Sally own two car dealerships, one in Los Angeles and one in San Francisco. 1. Los Angeles Let X = number of cars sold per day. Below is the probability distribution of the LA location. X 0 1 2 3 P(X) 0.4 0.3 0.2 0.1 a) Sketch and describe a histogram of the distribution. Describe the distribution. b) Calculate and interpret the mean of the distribution. c) Calculate the variance and calculate and interpret the standard deviation of the distribution. d) Suppose the dealership makes a profit of $4,000 per car. What is the mean and standard deviation of the daily profit? 2. San Francisco Let Y = number of cars sold per day. Below is the probability distribution of the SF location. Y 0 1 2 P(Y) 0.5 0.4 0.1 a) Calculate the mean, variance, and standard deviation of the number of cars sold in the SF location. 3. Combining Locations (Combining Random Variables) Now letâ€™s look at the distribution of the sales of the two locations combined. Let the total number of cars sold by Steve and Sally from both locations be represented by the equation T = X + Y a) As we will see later, we will need to assume independence between variables when combining random variables. What would it mean for the sales of the number of cars per day to be independent between the two locations? Do you think it is reasonable to assume so in this case? Briefly explain. b) Let the total number of cars sold be T = X + Y. Using the rules of independence, calculate the probability distribution below. (hint: there could be many different combos for each sum). T 0 1 2 3 4 5 P(T) c) Calculate the mean, variance, and standard deviation of the total number of cars sold. d) Compare the values in part c) to the mean, variance, and standard deviation of the LA and SF locations. What do you notice? e) What is the mean, variance, and standard deviation of the total profit, assuming they make $4,000 per vehicle? Big Ideas: