Please answer q's a, b, and c For each of the following proof excerpts, explain as fully as possible what the mathematicalstatistics context is, and what steps are being taken (i.e. relate it to the content being assessed).Standard notation for functions and parameters is used throughout. NB: you do not need tocomplete the proof.(a) Σxen (ag(x) + bh(x)) f(x) = a Σxen 9(x)ƒ(x) +bΣxenh(x)ƒ(x)(b) M"(t) = ²X(X – t)−¹ = & λ(A − t)−² = 2\(\ — t)−³ and M″(0) = 2/1/2dt2(c) P(Z² < x) = P( - √x < Z < √√x) = Fz(√x) – Fz( − √x)∞d(d) Σxpq* = pqΣxq-1 = pqdqx=0(e) F(2.5) 1 - e=-0.35x2.5∞d-1Σ9²Σ² = pq dq (1 — q)-¹x=0= 0.583 (3dp)nntxn-x(1) Σeta* (*) p² (1 − p)¹-² = Σ (*) (pe²)² (1 − p)¹−² = (1 − p + pe²)"n-xx=0x=0(g) F(x)=√x for 0 < x < 1 and F-¹(x) = x², so X = U²(h) E(et(a+bX)) = E(eat ebtX) = eªt Mx (bt)(i) [*²*¾a(2 − x)dx = ³ [x² − }x³[6]³ [2² - 2²³|²] = ³ (4- ) = 1(Ax)⁰e-A(j) P(X > x) = P(0 events in [0, x]) ==Xx= eso F(x) = 1 – e-λx-

Answered: Image /qna-images/answer/7018b37b-ee59-45a9-8612-5c8bc37ef44b.jpg

For each of the following proof excerpts, explain as fully as possible what the mathematical statistics context is, and what steps are being taken (i.e. relate it to the content being assessed). Standard notation for functions and parameters is used throughout. NB: you do not need to complete the proof. (a) Σxen (ag(x) + bh(x)) f(x) = aΣx€N 9(x)ƒ (x) + bΣxen h(x)ƒ(x) (b) M"(t) = X(X – t)−¹ = &A(A − t)−² = 2\(\ — t)−³ and M" (0) : - = dt2 (c) P(Z² < x) = P(-√√x < Z <√√x) = Fz (√x) - Fz( - √∞) ∞ (d) Σxpq* = pqΣxq²- x=0 x=1 (e) F(2.5) = 1 - e-0.35×2.5 n (f) Σ etx x=0 pª (1 − p)n-x = pq = ∞ d dq x=0 d q = pq (1 dq 0.583 (3dp) n n-x = • Σ(") (pet)ª (1 − p)"-" = (1 − p + pe¹)n x=0 -1 (g) F(x)=√x for 0 < x < 1 and F-¹(x) = x², so X = U² (h) E(et(a+bX)) = E(eat ebtX) = eat Mx (bt) (i) [ ²* ³ x (2 − x) dx = ³ [x² - 2³²12] = ³ (4-8) = 1 (j) P(X > x) = P(0 events in [0, x]) = (Ax)⁰e-Ax 0! -λx so F(x) = 1- e-λx

For each of the following proof excerpts, explain as fully as possible what the mathematical statistics context is, and what steps are being taken (i.e. relate it to the content being assessed). Standard notation for functions and parameters is used throughout. NB: you do not need to complete the proof. (a) Σxen (ag(x) + bh(x)) f(x) = aΣx€N 9(x)ƒ (x) + bΣxen h(x)ƒ(x) (b) M"(t) = X(X – t)−¹ = &A(A − t)−² = 2\(\ — t)−³ and M" (0) : - = dt2 (c) P(Z² < x) = P(-√√x < Z <√√x) = Fz (√x) - Fz( - √∞) ∞ (d) Σxpq* = pqΣxq²- x=0 x=1 (e) F(2.5) = 1 - e-0.35×2.5 n (f) Σ etx x=0 pª (1 − p)n-x = pq = ∞ d dq x=0 d q = pq (1 dq 0.583 (3dp) n n-x = • Σ(") (pet)ª (1 − p)"-" = (1 − p + pe¹)n x=0 -1 (g) F(x)=√x for 0 < x < 1 and F-¹(x) = x², so X = U² (h) E(et(a+bX)) = E(eat ebtX) = eat Mx (bt) (i) [ ²* ³ x (2 − x) dx = ³ [x² - 2³²12] = ³ (4-8) = 1 (j) P(X > x) = P(0 events in [0, x]) = (Ax)⁰e-Ax 0! -λx so F(x) = 1- e-λx

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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