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- Let X be the time in hours that the battery of a solar calculator functions properly between exposures to light sufficient to recharge it. Suppose the density of X is given by:f(x) = (50/6)x^-3 2 < x < 10.a) Verify that this is a valid continuous density. b) Calculate the expression for the cumulative distribution function of X and use it to calculate the probability that the charge of a randomly selected solar cell will last at most four hours before it needs to be used.at most four hours before it needs to be recharged. c) Calculate the average time that a battery charge lasts before it needs to be recharged. d) Calculate E[X2] and use its value to determine the variance of X. please only answer "d".Let f(x) is density function of continuous random variable x then the (expected value E(x Ek) = [ xfx)dx Ew) = [_fx)dx - 00 Ek) = ] -xfx)dx Ex)= | xf(x)dxLet X be the time in hours that the battery of a solar calculator functions properly between exposures to light sufficient to recharge it. Suppose the density of X is given by:f(x) = (50/6)x^-3 2 < x < 10.a) Verify that this is a valid continuous density. b) Calculate the expression for the cumulative distribution function of X and use it to calculate the probability that the charge of a randomly selected solar cell will last at most four hours before it needs to be used.at most four hours before it needs to be recharged. c) Calculate the average time that a battery charge lasts before it needs to be recharged. d) Calculate E[X2] and use its value to determine the variance of X.
- Suppose that X and X, have joint probability density function x2, if 1< xı < 2 and 1 < r2 < 3 10, fx1.x.("1, 2) = otherwise. What is the joint probability density function fy,y, of Y1 = X1/X2 and Y, = X2?For x1, the marginal distribution fx1 (x1) function is validis it a density function)Find k such that the function is a probability density function over the given interval. Then write the probability density function. f(x)=kx^2, [-4,2] k= f(x)=
- Let X be a continuous random variable with probability density function f(x) = 2(1-x), 0<=x <= 1. If Y = 2X - 1, find the probability density function of Y. x is lower case X is upper case. I need to get upper case of YSuppose that X₁ and X₂ have joint probability density finn 1x₁x2, if 1b) Suppose that the random variable X has a probability density function 0The life lengths of two transistors in an electronic circuit is a random vector (X; Y ) where X is the life length of transistor 1 and Y is the life length of transistor 2. The joint probability density function of (X; Y ) is given by ´2e-(x+2) x 2 0, y 20 fx,y(x,y)=| else Then the probability that the first transistor burned during half hour given that the second one lasts at least half hour equals Select one: a. 0.3935 b. 0.606 c. 0.7772 d. 0.3669 e. 0.6318Let Xbe a continuous random variable with density f (x) = 24x-4 for x > 2. Then Var (X) is equal toLet X₁, X2, X3, X30 be a random sample of size 30 from a population distributed with the following probability density function: f(x) = (0, -, if 0SEE 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