5. Given a normalized probability density function P(x) of finding the variable x in the interval [x, x + dx], write the definition for a) the mean value (x), b) the variance o? = ((x – (x))²), and c) the standard deviation of the variable x. %3D
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- 7. Let X be a continuous random variable with pdf f(x)=√ 0Please fast answer and correct answerIF it was XG (23) Independent of Xen G (13) Find Miley D-Probability density Function of the Variable YaX+Xq 2 -the Mean variance of the variableQ5 If P.d.f of It is given by f(x) = 1 e/sx i) e i) distribution function find iii). (v) P(X>1) 0Each day a random number, N ,of visitors make a purchase. The mean of N is E(N) = 12.8 and its variance is V(N) = 8.5 %3| Each of these visitors independently from the others spends a random amount of money, X; with mean E(X;)= 130.0 and variance V(X;) = 42.0 Let Y Σ Χ a day. be the total amount of money spent by visitors in the shop in Find the mean of Y and the variance of YQuestion 2: Can you answer this questionThe density function of X is -120x- 0, f(x) = (2(x - 1), (a) Find the mean E(4X+3); (b) Find the variance 3x+2. 1 < x < 2, elsewhere.C1. Let X be a continuous random variable with PDF f(x) = ? (2 – a) for –1 1)? (c) Calculate the expectation and variance of X. (d) Let Y (X2 – 1). What is the expectation of Y?1. Let X have the pdf f(x) = B-lexp{-x/B}, 0 < xSEE 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