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- Find the average rate of change for each function over the given interval. y=1x1 between x=2 and x=0Find the average rates of change of f(x)=x2+2x (a) from x1=3 to x2=2 and (b) from x1=2 to x2=0.Figure I shows the piecewise function (I), (II), (III) and (IV) for cumulative distribution function F(x) for continuous random variable. F(x) (6. 1) IV III II (4.0.8333) (0.0.1667) Figure I Construct the probability density function fix). Should one of the piecewise functions (IV) is not constant, explain the changes.
- Let X = b(16,- find E(4- 3x) and distribution function.Determine the values of A and B that f (x) continuous A = B =Q1 Let (X₁, X₂) be jointly continuous with joint probability density function " f(x1, x₂) = x1 0Find 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)= Find the marginal PDFs of X and Y.The probability density function of a distribution is given by x f(x) = exp(-7). Use differentiation to show that the probability density function has a maximum at x = 0. The moment generating function of a distribution is M(t) = (q + pet)", where p € [0, 1], q = 1 - p and n is a positive integer. Use the moment generating function to find the mean and variance of the distribution in terms of p, q and n.Find the mean and standard deviation for each uniform continuous model U(1, 13) U(70, 200) U(3, 92)7. Assume that X and Y have joint probability density function given by (2x + 3y) if 0< x<1 and 0Indicate whether the function could be a probability density function. Explain. S6x(7 – x²) when 0 sxs 1 g(x) elsewhere The graph---Select--- O a probability density function because ---Select--- 1. (x)ESEE MORE QUESTIONSRecommended textbooks for youCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage LearningCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning