Show more Observation No. X1 X2 1 1492.0 1668.1 2 1538.8 1728.4 3 1621.9 1797.4 4 1689.6 1916.3 5 1674.0 1896.6 6 1711.9 1931.7 7 1803.9 2001.0 8 1883.8 2066.6 9 1961.0 2167.4 10 2004.4 2212.6 11 2000.4 2214.3 12 2024.2 2248.6 13 2050.7 2261.5 14 2146.0 2331.9 15 2249.3 2469.8 16 2354.8 2542.8 17 2455.2 2640.9 18 2521.0 2686.3 1. What is the value of X92? 2. Calculate 18 sigma i=1 Xi2 3. Calculate 2 sigma j=1 X4j 4. Calculate 18 sigma i=1 (multiplied by) 2 sigma j=1 Xij 5. Is X1 a continuous variable? 6. There are 30 students enrolled in this class. Suppose Hi is the height of the ith student. What is the range of values for i? Is Hi a random variable? 7. The following is the joint probability distribution of number of car crashes (C) and car make (M). C = 0 C = 1 C = 2 C = 3 C = 4 TOYOTA (M = 0) 0.35 0.065 0.05 0.025 0.01 OTHER (M = 1) 0.45 0.035 0.01 0.005 0.00 A. Report the marginal probability distribution for C B. What is the average number of car crash? C. What is the variance of the number of crashes? D. Calculate ?CM and ?CM. 8. Suppose car manufacturers are penalized (P) on the basis of the following formula P = 60000 + 6C 2M Using your answers for Question 7 calculate the following The average penalty (P) The variance of penalty (P) 9. X and Y are two random variables. The average value of X is 40000 and X has a standard deviation of 12000. The average value of Y is 45000 and the standard deviation of Y is 18000. The correlation between X and Y is 0.80. Let C = X + Y Calculate E(C) Cov(XY) Var(C) 10. The random variable Y has a mean of 1 and a variance of 4. Let Z = (Y 1) Calculate Z and ?Z 2 . Show less