4. Suppose that n balls are randomly distributed in N compartments. Find the probability that m...
4. Suppose that n balls are randomly distributed in N compartments. Find the probability that m balls will fall in the first compartment. Assume that all N" arrangements are equally likely.
Covariance: Suppose 10 balls are randomly distributed into 4 urns. Let Xj be the number of balls that fall into the jth urn, and let Ti be the indicator variable that the ith ball falls into jth urn, with E {1, . . . , 10} and j є {1, . . . , 4). ·P(X, = 0) =? (hird
1) Suppose that three balls are sampled without replacement from an urn containing 5 red balls and 5 green balls. Find the probability that the sample contains at least one ball of each color 2.) Suppose that a pair of fair dice is rolled and that all 36 outcomes are equally likely. Calculate the probability that the second die lands on a number greater than the first.
Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 264 feet and a standard deviation of 45 feet. Let X be the distance in feet for a fly ball. a. What is the distribution of X? X ~ N(,) b. Find the probability that a randomly hit fly ball travels less than 229 feet. Round to 4 decimal places. c. Find the 70th percentile for the distribution of distance...
An urn contains M white and N black balls. Balls are randomly selected, one at a time, until a black one is obtained. If we assume that each ball selected is replaced before the next one is drawn, what is the probability that a) exactly x draws are needed? b) at least k draws are needed?
10. Use Rubber Balls in a Box Setup. Suppose 5 rubber balls are to be randomly drawn out (all at once). Find the probability that the numbers on the rubber balls will be sequential (when, after drawing, the numbers are arranged lowest to highest). This is a short answer question. The correct answer is a fraction. It is NOT NECESSARY to simplify the answer. 11. Use Rubber Balls in a Box Setup. Suppose 3 rubber balls are to be randomly...
Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and a standard deviation of 50 feet. We randomly sample 49 fly balls. (a) What is the probability that the 49 balls traveled an average of less than 240 feet? (Round to 3 decimal places) (b) Find the 80th percentile of the distribution of the average of 49 fly balls.
Each of k jars contains m white and n black balls. A ball is randomly chosen from jar 1 and transferred to jar 2, then a ball is randomly chosen from jar 2 transferred to jar 3, etc. Finally, a ball is randomly chosen from jar k. Show that the probability that the last ball is white is the same as the probability that the first ball is white, i.e., it is m/(m+n) . (Hint: Prove the result for K=2...
Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 256 feet and a standard deviation of 41 feet. Let X be the distance in feet for a fly ball. a. What is the distribution of X? X-NG b. Find the probability that a randomly hit fly ball travels less than 333 feet. Round to 4 decimal places. c. Find the 85th percentile for the distribution of distance of fly...
Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 238 feet and a standard deviation of 44 feet. We randomly sample 49 fly balls. A) What is the probability that the 49 balls traveled an average of less than 226 feet? (Round your answer to four decimal places.) B) Find the 60th percentile of the distribution of the average of 49 fly balls. (Round your answer to two decimal...