The following formula defines a joint probability density func- tion. What is the value of C? What are the expected values ux and μγ SCxy, if 0 < x < 2 and 0 < y < 3, lo, f(x, y) = otherwise.
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- One of the important properties of the probability density function, f(x), of a random variable X is f(x) 2 0, for all values of X. Select one: O True O False PAGEAnswer all the questions. Suppose that during periods of moditation the redhuction of a person's oxygen cansumption is a random variable having the following probability density function Sx)- f(x) if-2Which of the following tables shows a valid probability density function? Select all correct answers. Select all that apply: x P(X=x) 0 0.6 1 0.01 2 0.14 x P(X=x) 0 310 1 110 2 25 x P(X=x) 0 18 1 14 2 58 x P(X=x) 0 0.13 1 0.09 2 0.45 3 0.27 4 0.06 x P(X=x) 0 −15 1 310 2 12 3 310 4 110 x P(X=x) 0 12 1 18 2 38Let μx and of be the expectation and variance of a forecast model F for an observations y, and let pÃ(.) denote the probability density function for the forecast model. Also let G be a different forecast model. Which of the following statements are true? a. Two forecast scores S(F, y) and S(G, y) are independent. b. The square error (y – µµ)² is a proper score. C. The score (y - μF) ²/0 is proper score that improves in the squared error score by taking the variance into account. d. The logarithmic score – log[pf(y)] is a strictly proper score. -Let the Probability Mass Function as follows: f(-1)=0.2, f(2)=0.3, f(3)=0.35 and f(0)=??, Then F(2)- a 0.35 O b.0.65 c0.15 d. 0.3 geQ.2 Let X has the following probability density function: fx(x) = a e-ax;x > 0 Find moment generating function and then using it find mean and variance. End of QuizWhy is P(X = c) = 0 for any number c in the domain of a probability density function?For a random variable which can be defined using the probability density function below, what is the probability that X is between 1.5 and 3.2? f(x) = {C(1+ x) ,1Find the mean and variance of X given the following probability density function:Verify Property 2 of the definition of a probability density function over the given interval. 1 10 f(x)= [4,6]Let fx(x) be the probability density function of the random variable X. 3 22-4< e< 4; Ka) - f(z) = { 128 otherwise. Determine the E{X}. [The answer should be a number rounded to five decimal places, don't use symbols such as %SEE MORE QUESTIONSRecommended textbooks for youCalculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSONCalculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage LearningCalculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSONCalculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning