You are given the following information regarding random variable X: I. E[X] = 2 II. E[X*] = 10 III. Var[X] = 1 Find E[(X – 1) ³].
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- An interpolation function, P(x), for e 2 x between x=0 and x=.5 was found using the following data points (0, 1), (0.1, 1.2214), (0.2, 1.4918), (0.3, 1.8221), (0.4, 2.2255), and (0.5, 2.7183). What is the upper bound of the approximation at P(0.25)? a) ( 0.25 ) ( 0.25 – 0.1) ( 0.25 – 0.2 ) ( 0.25 – 0.3 )( 0.25 – 0.4 ) (0.25 – 0.5 ) 6 ! 2 6 e 0.5 b) ( 0.25 ) ( 0.25 - 0.1) (0.25 – 0.2 ) ( 0.25 - 0.3 ) ( 0.25 – 0.4 ) ( 0.25 – 0.5 ) 5!25 e 0.5 c) ( 0.25 ) ( 0.25 – 0.1) ( 0.25 – 0.2 ) ( 0.25 – 0.3 ) (0.25 – 0.4 ) ( 0.25 – 0.5 ) 6 ! 2 6 e d) ( 0.25 ) ( 0.25 – 0.1) ( 0.25 – 0.2) ( 0.25 – 0.3 ) ( 0.25 – 0.4)( 0.25 – 0.5 ) 5 ! 25 e - - (0.25)(0.25-0.1)(0.25-0.2)(0.25-0.3)(0.25–0.4)(0.25–0.5) ,6 ,0.5 6! (0.25)(0.25–0.1)(0.25–0.2)(0.25–0.3)(0.25,0.4)(0.25–0.5) 25 0.5 5! O (0.25)(0.25–0.1)(0.25–0.2)(0.25-0.3)(0.25-0.4)(0.25–0.5) -26e 6! (0.25)(0.25–0.1)(0.25–0.2)(0.25–0.3)(0.25–0.4)(0.25–0.5) ,5. 5!(d) Experiment: measure the quantities a, b, c (in cm) of rainfall in a day at each of three weather stations A, B and C. Event: it is driest at station A. 2. Suppose we have 2=[0,9]={xR;0Suppose that Y is an exponential random variable with λ = 4. Find. P[Y > (E(Y) + 2√√Var(Y))] . (round to 4 decimal points)Problem 7 A new formulation of concrete has been designed for a particular building application. Naturally, the strength of concrete produced with the new formulation had to be tested for its strength capability. The compressive strength of 12 specimens were tested, as shown below. 2216 2281 2237 2263 2249 2318 2204 2255 2225 2275 2301 2295 a. With a simple histogram, draw conclusions about the normality of these observations. Assume normality regardless. b. Calculate a 95% confidence interval for mean compressive strength. c. Calculate a 95% confidence interval for standard deviation of compressive strength.Q1. let Y₁ < Y₂ < Y3 < Y4 < Y5 are the order statistics of the random sample of size 5 from the distribution : f(x) = 3x², 03. Let X1, and E- X; are independent. , Xn be iid with exponential distribution with mean 0. Show that (X1+X2)/ E=1 X;6. Find the mean and variance of fx (x) = 2e eA* la.2...) (x) = de(a) Let Y be a random variable distributed as X. Determine E(Y) in terms of r. (b) Let {X1, X2, . .. , Xn} be a random sample drawn from a normal distirbution with mean u and 1 variance o?. Denote S E-(X; – X)² as the sample standard deviation. Use the 1 n - result in part (a), or otherwise, to find E(S). (c) Find an unbiased estimator for the population standard deviation o.4. Let X be a positive random variable (i.e. P(X 1/E(X) (b) E(-log(X)) > -log(E(X)) (c) E(log(1/X))> log(1/E(X)) (d) E(X³) > (E(X))³4. Find the mean of the discrete random variable X with the following probability distribution. Use this formula. μ -ΣΙΧ . P (X)] P(x) х. Р(х) x2 x² . P(x) X 14 1 /½ 5. Referring to the table above, solve for the variance and standard deviation. Use this formula. o² = E[x2 . P(X)1 – µ? E[x² - P(X)] – µ² | O =SEE 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