The random variableX has the following continuous probability distribution in the range 0 < x < k - 4 (where k is a positive number) is shown in the coordinate plane with X on the horizontal axis. f(x) k -1.5 3 -- k – 4
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- you should calculate the required probabilities using tables A model for normal human body temperature, X, when measured orally in F, is that it is normally distributed, X N(98.2, 0.5184). According to the model, what proportion of people have a normal body temperature of 99 F or more? (0) (i) Find the normal body temperature such that, according to the model, only 10% of people have a lower normal body temperature. (ii) Let W denote normal human body temperature, when measured orally in C. Given that W =59 (X-32) and X N(98.2, 0.5184), what is the distribution of W?[Q1] The probability distribution of the discrete random variable X is: f(X) = k23-* , for x = 4,5, 6, 7 (a) Find: • the value of the constant k. • The mean E (X). • The variance Var(X). (b) Sketch F(X).A shipment of 7 television sets contains 2 defective sets. A hotel makes a random purchase of 3 of the sets. If X is the number of defective sets purchased by the hotel, (a) find the probability distribution of X, express it in a table format. Probability distribution of X X P(X) (b) Find the cdf of X. (c) Find the E(X) and Var(X)
- Let X be a random variable with the following probability f(x) = c(1 – 2x2 + x3), x = 0, 1, 2, 3, 4, 5. Find the value of c to make it a probability Establish the probability distribution of X (table). Find the mean of the random variableLet X denote a random variable having a distribution. If F(x)=ax³ where 0≤x≤(+3). Find f(x) after getting the constant value (a) and find the probability P(2Find p(x) for x=0,1, 2, 3, 4, 5.Q1A Suppose that the probability of finding defectives within a manufactured lot of electrical fuses is 0.09. Assume the probability distribution function (PDF) is binomial. Let X be the number of defectives within the sample. In a sample of 25 fuses, find the probabilities: (a) P(X 2), (b) P(X > 0), (c) P(1 ≤ X < 4). === B Suppose the discrete random variable X has the PDF as in the table below. Find: (a) F(7), (b) E(4-3X). I 4 6 7 8 9 f(x) 0.2 0.25 0.15 0.3 0.1let x be a discrete random variable with probability function p(x)= cx/20 for x = 2,3,4,5,6,8,12 what is the value of c that makes p(x) a valid probability function?The probability distribution function of a random variable X is 4. P(X =x)=Dk for x=0,1, 2,3,4 where k is a constant. Determine (a) the value of k. Hence, find P(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