Random variable X has density f(x) = e-kl, a) Sketch the graph of f (x). b) Find P(|X|< 4).
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![Random variable X has density f(x) =e-#l.
a) Sketch the graph of f (x).
b) Find P(|X|< 4).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faeb3e818-56ab-4527-a46f-eb6c0eabaf41%2F79d1ae2e-c5f3-4b76-ac96-0408d26ff191%2Fagv0k3_processed.png&w=3840&q=75)
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- 1)A random vector z = (x y) T has joint probability density given by:a)Sketch the graph of the probability density function pxy(X, Y ).b)Determine the value of the constant C.c)Determine the mean mz vector.Given the Rayleigh random variable with density function show that the mean πρ V4 E[X] =a + CS Scanned with CamScanner f(x) -(x-a)² b 2 =(x-a)e u(x -a)A random variable X has a density function (cx² f (x) = {cx 1 2) P(1/2Exercise 40 Let X Unif(0,1). Let g(x) = e" and Y = g(X). (i) Find the density fx of the random variable X. (ii) Find the cdf Fy (y) = P(Y < y) of Y. (iii) Find the density fy of the random variable Y.function f (x, y) =15e-2x-3y a joint probability density function over the range 0While taking a walk along the road where you live, you accidentally drop your glove, but you don't know where. The probability density p(x) for having dropped the glove a kilometers from home (along the road) is p(x) = 2e-2 for x ≥ 0 a. What is the probability that you dropped it within 1 kilometer of home? I b. At what distance y from home is the probability that you dropped it within y km of home equal to 0.95? km <-|L The projection X of the radius-vector of a random point on a circumference of radius a onto the diameter has the distribution function (the arcsine law) F(x) { +arcsin for-a< x <6; Determine (a) the probability that X will be on the interval (—a/2, a/2), (b) the quantile x0.75, (c) the probability density f(x) of the random variable X, (d) the mode and median of the distribution.A continuous random variable X has density function f(x) = 1.5(1 – x²), 0 < x < 1. a) Calculate the expected value of X. b) Calculate the expected value of X?. c) Calculate the standard deviation of X. d) Calculate the expected value of Y = 4X + 5. e) Calculate the standard deviation of Y = 4X + 5.A continuous random variable X has cumulative distribution function F(x) = 1 – e-0.8z, x > 0. a) Find the density function of X. f(x) z >0 b) Find the probability that X 3. d) Find the probability that X = 5.function Let the random variables X and Y follow a joint density { 20+7, 0, fxy(x, y) = 0 < xRecommended 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