|A9 a) The continuous random variable Xhas probability density function f(x) = ®(1– x)®-1 , 00 ) Find the cumulative distribution function, F(x), of X i) Find P(0.25
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- A random variable X has a distribution function I 1. Find its 1) coefficients A, B, 2) distribution density f(r), make plots of both F(r) and f(r), 3) mathematical expectation, variance.please solve c partRandom variable X-N(2,1). New random variables are defined as Y = 4X +1 and Z = X+Y. a) P(Z <1) = ? b) E[Z] =? c) var (Z)= ? d) Give the probability density function of Z (proof is not required). e) Sketch the probability density function and cumulative distribution function of Z.
- (****) A continuous random variable X has probability density function (PDF) for some constants a and b. If Pr(X ≤ 0) is 2 times Pr(X > 0), what are a and b? a= b = f(x) = Jae for x < 0 (bxe-x² for x ≥ 0Which of the following are continuous variables, and which are discrete?(a) Speed of an airplane(b) Age of a college professor chosen at random(c) Number of books in the college bookstore(d) Weight of a football player chosen at random(e) Number of lightning strikes in Rocky Mountain National Park on a given daydo al otherwise not
- 3- Remission time for a certain group of leukaemia patients (X, measured in months) Has cdf 0, F(X) = {₁º- e-x/³, x < 0 x ≥ 0 a) Find the pdf b) What is the probability that a random selected patient will be in remission for 2 to 5 month?A continuous random variable has probability density function given by K(2x-3);1<x2 Find k if f(x) is a probability density functionThe distribution function for a random variable X is -2х F(x) = 1 - e 2x, x > 0 , X 2 c) the probability that -3 < X <4
- 7The probability density function for the continuous random variable X is given by: (А(х? — 2х + 21) 0The total number of hours, in units of 100 hours, that a family runs a vacuum cleaner over a period of one year is a random variable X having the density function shown to the right. Find the variance of X (x-8). f(x)2-(X-8). 9sx< 10, 8Recommended 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