Consider the probability density function f(x) = 1.5x² for-1 ≤x≤ 1. What is P(x > 0)? a. 0 b. 0.125 c. 0.25 O d. 0.5
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- Solve using R. Show all work.Answer all the questions. Suppose that during periods of moditation the redhuction of a person's oxygen cansumption is a random variable having the following probability density function Sx)- f(x) if-2please solve c partWhich of the following tables shows a valid probability density function? Select all correct answers. Select all that apply: x P(X=x) 0 0.6 1 0.01 2 0.14 x P(X=x) 0 310 1 110 2 25 x P(X=x) 0 18 1 14 2 58 x P(X=x) 0 0.13 1 0.09 2 0.45 3 0.27 4 0.06 x P(X=x) 0 −15 1 310 2 12 3 310 4 110 x P(X=x) 0 12 1 18 2 38The table below shows an incomplete probability density function for X , the number of imperfections per batch of jeans that just came off a production line. What should the missing probability be? Provide the final answer as a decimal. x P(X = x) 0 0.88 1 0 2A somewhat outdated study indicates that the mean number of hours worked per week by software developers is 44. We have good reason to suspect that the mean number of hours worked per week by software developers, u, is now greater than 44 and wish to do a statistical test. We select a random sample of software developers and find that the mean of the sample is 47 hours and that the standard deviation is 4 hours. Based on this information, complete the parts below. (a) What are the null hypothesis H, and the alternative hypothesis H, that should be used for the test? H, :0 OThe probability density function for a continuous random variable X is given by 0 < x < 1 1≤ x ≤ 2 else Find P(0.5 < X < 1.5) Round to 4 decimal places if needed. f(x) = X 2-xQ16C onlyFor a random variable which can be defined using the probability density function below, what is the probability that X is between 1.5 and 3.2? f(x) = {C(1+ x) ,1Suppose that the random variable X has the probability density function for -1 < x s 1 c(1- x2) f(x) = elsewhere Find the value of the constant c. Ans is Blank 1 Blank 1 Add your answerThe table below shows the probability mass function of the amount of memory X (GB) in different flash drives available in a certain store. 1 .25 y p(y) What is the V(Y) a. 0.25 Ob. C. 0 d. 0.74 .60 0.85 None of the answers 2 .10 3 .05For a random variable which can be defined using the probability density function below, what is the probability that X is between 1.3 and 3.1? с (1 + х) ,1 <SEE MORE QUESTIONSRecommended 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