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- The following function is a cumulative distribution function. x < -10 0.1510. Find the moment generating function about origin of the Poisson distribution.Let X be b(2, p) (binomial distribution). Assume P(X > 1) = (a) Find p. (b) Compute P[X = 2]. %3DThe following table is a partial probability distribution for the MRA Company's projected profits (x = profit in $1,000s) for the first year of operation (the negative value denotes a loss). x f(x) −100 0.100 0.2050 0.30100 0.25150 0.10200 (a) What is the proper value for f(200)? f(200) = What is your interpretation of this value? This is the ---Select--- percent probability that the MRA will have a $200,000 profit. (b) What is the probability that MRA will be profitable? (c) What is the probability that MRA will make at least $100,000? Please only correct and with concept and dont do handwritten or skip please!!The maintenance department in a factory claims that the number of breakdowns of a particular machine follows a Poisson distribution with a mean of 2 breakdowns every 428 hours. Let x denote the time (in hours) between successive breakdowns. (a) Find λ and Ux. (Write the fraction in reduced form.) ux = f(x) = 214 (b) Write the formula for the exponential probability curve of x. P(x <4) ✔ Answer is complete and correct. 1 P(115Consider the curve below 0.2- 1 2 3 4 5 6 Find the probability that x < 2 P (x < 2) =B. Find the following probabilities using the t-table if X~t20 a. P(T > 0.860) b. P(T < - 1.325) C. Find k such that P(k< T< 2.947) = 0.845 when T~t15The time (in minutes) between arrivals of customers to a post office is to be modelled by the Exponential distribution with mean 0.62. a) find the P(10<x<15) (10 and 15 are seconds) b) find the P(x>15| x>10) (10 and 15 are seconds) c) find the P(x<15) (15 is seconds)Recommended 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