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solve parts 4, 5, 6 please
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- Find 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.Find the average rate of change for each function over the given interval. y=1x1 between x=2 and x=0Figure 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.
- 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)= Q1 Let (X₁, X₂) be jointly continuous with joint probability density function " f(x1, x₂) = x1 0Q1 Let (X₁, X₂) be jointly continuous with joint probability density function 0 < x2 < x1 < 1, otherwise. f(x1, x₂) = x1 0 Q1(i.) Sketch(Shade) the support of (X₁, X₂). Q1(ii.) Find the marginal density function of X₁. Q1(iii.) Find the marginal density function of X₂. Q1(iv.) Find E[X₁]. Q1(v.) Find E[X₂]. Q1(vi.) Find the conditional density of X₂ given X₁ = x₁, i.e., fx₂x₁ (x₂|x₁). Q1(vii.) Find the conditional expectation of X₂ given X₁ x₁, i.e. E[X₂|X₁ = x₁]. = Q1(viii.) What is E[X₂X₁]? Using the property of conditional expectation, verify that E[X₂] is the same as the one obtained in part Q1(v.). Q1(ix.) Using the joint density directly, find E[X₂] and verify that it is the same as obtained Q1(v.) and Q1(viii.). Q1(x.) Using the joint density directly, find E[X₁ — X₂]. Q1(xi.) Using the joint density directly, find E[X₁ X₂], and the Cov(X₁, X₂).* Consider the probability density function fx (x) = a e-b lel where X is the random %3D variable which assumes all the values from (i) relation between a and b -00 to -00, Find (ii) the probability of finding X in the range 1 to 2.7. 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)EThe lifetime of a machine part has a continuous distribution on the interval (0,45) months with probability density function f, where f(x) is proportional to (4+x)-2. Find the probability that the lifetime of the machine part is less than 7 months.Let X = b(16,- find E(4- 3x) and distribution function.Show that f(x)f(x) is a probability density function, Find E(X)E(X) and Var(X)Var(X).SEE 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