A. State Bayes Theorem B. There are three cookie jars in the kitchen, a blue jar, a red jar, and a green jar. The blue jar contains 10 ginger snaps and 11 chocolate chip cookies. The red jar contains 9 ginger snaps and 12 chocolate chip cookies. The green jar contains 10 ginger snaps and 13 chocolate chip cookies. In the middle of the night, Sam goes to the kitchen and chooses a jar without turning on the light and gets a cookie from it. Find the probability that the cookie came from the blue jarprovided the selected cookie was chocolate chip. 2. Compute E(x) and o(x) if x follows the following probability distribution X 0 1 2 3 4 p(x) 0.1 0.2 0.3 0.2 3. A die is tossed 100 times. Find the probability that "1 or 3" shows up. A) Exactly 30 times. B) At least 30 times. 4. Through a survey, it was found that the average intake of medicine in a large group of patients 250 mg per week with a standard deviation of 20 mg per week. A) A patient is chosen at random. Find the probability that his or her intake exceeds 240 mg per week. B) 3 patients are chosen at random. Find the probability that their average intake is between 245 mg and 255 mg per week. 5. A die is tossed 100 times. Find the probability that "2 or 4" shows up at least 40 times. Do this problem as a normal distribution. 6. Find the coefficient of variation of the data: 10, 17, 15, 23, 217. Find the mean of the data: Class Frequency 0-10 12 10-20 28 20-30 40 30-40 22 40-50 17 50-60 10 8. Compute Cov(x, y) if (x, y) follows a joint distribution P(x, y) given below: 0 0.2 0.3 2 0.4 0.1 9. Compute p(x, y) if (x, y) follows a joint distribution P(x, y) given below: 0 0.2 0.3 2 0.4 0.1 10. There are 300 misprints in a 500-page book. Find the probability that A) a particular page contains exactly 2 misprints. B) a particular page contains more than 2 misprints. 11. What is the smallest value of & in Tchevishev's Theorem for which the probability Prob( H - ko