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- 4. A particle performs a random walk on the vertices of a cube. At each step it remains where it is with probability, or moves to one of its neighbouring vertices each having probability 1. Let v and w be two diametrically opposite vertices. If the walk starts at v, find: (a) the mean number of steps until its first return to v, (b) the mean number of steps until its first visit to w, (c) the mean number of visits to w before its first return to v.1. Let X ~ Poisson(A) and Y ~ Poisson(u). Assume that X and Y are independent. Use probability generating functions to find the distribu- tion of X + Y.4. Assume the below life table was constructed from following individuals who were diagnosed with a slow-progressing form of prostate cancer and decided not to receive treatment of any form. Calculate the survival probability at year 1 using the Kaplan-Meir approach and interpret the results. Time in years Number at risk Nt Number of deaths, Dt Number of censored Ct Survival Probability 0 20 1 1 20 3 2 17 1 3 16 2 1 A) The probability of surviving 1 year after being diagnosed with a slow-progressing form of prostate cancer is .85.B) The probability of surviving 1 year after being diagnosed with a slow-progressing form of prostate cancer is .85 for the individuals being followed in this study.C) The probability of surviving 1 year after being diagnosed with a slow-progressing form of prostate cancer is .85 for individuals who decided against all forms of treatment.D) The probability of surviving 1 year after being diagnosed with a slow-progressing form of…
- 23. *An insurance policy pays an individual 100 per day for up to 3 days of hospitalization and 25 per day for each day of hospitalization thereafter. The number of days of hospitalization, X, is a discrete random variable with probability function Pr(X = k) = (1/15)(6 – k), k = 1, 2, 3, 4, 5. Calculate the expected payment for hospitalization under this policy. (213.3)24. Use the probability distribution to complete parts (a) through (d) below. The probability distribution of number of televisions per household in a small town X 0 3 P(x) 0.03 0.54 (a) Find the probability of randomly selecting a household that has one or two televisions. The probability is (Type an integer or a decimal. Do not round.) (b) Find the probability of randomly selecting a household that has two or more televisions. 1 0.11 2 0.32 The probability is (Type an integer or a decimal. Do not round.) (c) Find the probability of randomly selecting a household that has between one and three televisions, inclusive. The probability is (Type an integer or a decimal. Do not round.) (d) Find the probability of randomly selecting a household that has at most two televisions. The probability is (Type an integer or a decimal. Do not round.)13. A continuous random variable is uniformly distributed between 200 and 220. a. What is the probability a randomly selected value will be greater than 215? b. What is the probability a randomly selected value will be less than 205? c. What is the probability a randomly selected value will be between 205 and 215? a. P(x > 215) = (Simplify your answer.) b. P(x< 205) = (Simplify your answer.) c. P(20523. Find the cumulant generating function of gamma distribution and obtain various cumulants.12. The number of new individuals in a population of animals is sometimes approximated calculating the expected number of survivors of the new born animals from the next genera- tion. The idea is that the number of new animals born follows some probability distribution, and the number of animals that survive depend on how many are present.¹ One example of a survivor function is the following: S₁(k) = b.ck, where b and c are real numbers with 0Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th…StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C…StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage LearningElementary Statistics: Picturing the World (7th E…StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. FreemanMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th…StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C…StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage LearningElementary Statistics: Picturing the World (7th E…StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman