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- Which of the following validates a probability density function?* all f(x) must be greater than or equal to 0 all f(x) must be less than or equal to 1 the integral of the probability density function must be equal to 1 from its lower limit to its upper limit the sum of the probabilities of f(x) must be equal to 1 all of the choicesHow do I tackle such a problemSince height is a continuous numerical variable, its probability density function is represented by the smooth curve below. What is true about the area under the curve? 140 160 180 200 height (cm) The area does not represent all possible heights, so the area under the curve and probability are both 0. O The area does not represent all possible heights, so the area above the curve is 1. O The area represents all possibile heights, so the area and probability are both 100. The area represents all possible heights, so the area under the curve and probability of all the height occurring are both 1.
- сх, f(x)= 0Please answer all of the questions by showing calculationsWhy is P(X = c) = 0 for any number c in the domain of a probability density function?The 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-xsolve Last 2 questions pleaseSuppose 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 answerRecommended 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