5. Let X be an arbitrary set, and define u on P(X) by 0 if A=0 μ* (A) = Prove that is an outer measure. {"d 1, otherwise
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- asap guysLet f(x) = 1+ x² + x4 + •…+ x²k (k € Z+ u {0}). For what value of k, mean value of f (x) is on [-1,1] ? 23 15 A) k = 1 B) k = 2 C) k = 3 D) k = 4 E) k = 5 %3Di.i.d. Let X1, X2, ..., X„ " i. Find a two-dimensional sufficient statistic T(X) for a and B. gamma(a, B), a > 0, B > 0. ii. Show that T is minimal sufficient. iii. Show that T is complete.
- 4.08 Consider Y with pmf p(y) = exp(-3.8)(3.8)'-2/(y-2)! defined on some set. ( a Determine a valid set. ( b Calculate P(Y > 3).12. Let f20 and measurable over E. Let et [₁ E f = 0. Prove that f = 0 a.e. Hint: Consider {z € E : ƒ (2) > 0} = Ů { x € E : ƒ(x) > } } n=1 Inequality. and remember Chebychev'sQ1: Find Sup ; Inf; Max; Min for the following sets: m { e z*} . (a) S = 2n : m,n E Z* }; (b) T = {n+1 :n E Z+ Q2: (a) Let a ,b E R, and a < b. Prove that 3s ER- Q, a11. A finitely additive measure u is a measure iff it is continuous from below as in Theorem 1.8c. If μ(X) < oo, u is a measure iff it is continuous from above as in Theorem 1.8d.1.2. Let X, d be a complete metric space, f: X→ X a function satisfying d(f(x1), f(xo)) ≤ Ld(x1, xo) for all xo, 1 EX = I. for some L< 1. Show that there is x EX such that f(x) =16. If S ST S R, where S + 0, then show that (i) If T is bounded above, then sup SRecommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEYMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,Advanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEYMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,