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2. Let S-{a,b,c,d) and let F1, F2 be ơ-algebras of subsets of S2 given by a....
Let M be a ơ-algebra of subsets of X and P the set of finite measures on M. Prove that (a) d(μ, v) = supAEM |μ( A)-v(A)| defines a metric on P (b) (P, d) is complete. Let M be a ơ-algebra of sub...
Let M be a ơ-algebra of subsets of X and P the set of finite measures on M. Prove that (a) d(μ, v) = supAEM |μ( A)-v(A)| defines a metric on P (b) (P, d) is complete.
Let M be a ơ-algebra of subsets of X and P the set of finite measures on M. Prove that (a) d(μ, v) = supAEM |μ( A)-v(A)| defines a metric on P (b) (P, d) is complete.
Three forces acting on an object are given by F1 = (-1.551+ 5.70j N, F2 4.55-1.8j)...
Three forces acting on an object are given by F1 = (-1.551+ 5.70j N, F2 4.55-1.8j) N, and F3 -42i) N. The object experiences an acceleration of magnitude 3.85 m/s2 (a) What is the direction of the acceleration? (counterclockwise from the +x-axis) (b) What is the mass of the object? kg (c) If the object is initially at rest, what is its speed after 19.0 s? m/s (d) What are the velocity components of the object after 19.0 s? (Let...
(a) State what is meant by saying that F is a σ-field on a set Ω. I. (b) Let F1 and F2 be two-fields on a set Ω. Is Ћ UF2 a-field on Ω? If yes, show that Fİ UF2 is a σ-field on Ω. If not, give a coun...
(a) State what is meant by saying that F is a σ-field on a set Ω. I. (b) Let F1 and F2 be two-fields on a set Ω. Is Ћ UF2 a-field on Ω? If yes, show that Fİ UF2 is a σ-field on Ω. If not, give a counterexample. , isaơ-field on . (c) Let 2-11,2,3,4,5,6,7,8,9,10) and F(A) be the o-field generated by A - 11,2,3,5, 10), 2,8,51, 16,7)1 (i) Find F(A); (ii) Give an example of four-fields F1,...
2. Given the set S-ta,b,c,d,e,f,g,h) a) How many subsets does S have? b) How many subsets...
2. Given the set S-ta,b,c,d,e,f,g,h) a) How many subsets does S have? b) How many subsets have exactly 5 elements? c) A subset is randomly chosen for the collection of all possible a) b) c) subsets. What is the probability that it contains exactly 3 elements? d) A subset is chosen at random from all the subsets. d) What is the probability that it contains the element a?
2. Let A and B be subsets of a sample space S. The relative complement of...
2. Let A and B be subsets of a sample space S. The relative complement of B with respect to A is denoted and give by A B(r:r E A and r (a) Express B as a relative complement. (b) Prove that A B An B. (c) Prove that (A\B) A*UB. (d) Prove that p(AP)-P(1)-P(An B). B).
Let S be the universal set, where: S = {1, 2, 3, ..., 18, 19, 20}...
Let S be the universal set, where: S = {1, 2, 3, ..., 18, 19, 20} Let sets A and B be subsets of S, where: Set A = {2,5, 6, 7, 8, 14, 18} Set B = {1, 2, 3, 4, 7, 9, 10, 11, 12, 14, 18, 19, 20} Find the following: The cardinality of the set (A U B): n(AUB) = The cardinality of the set (A n B): n(An B) is You may want to draw...
2. (a) Let B = {f1, f2, f3} be a subset of P2 where fi(x) =...
2. (a) Let B = {f1, f2, f3} be a subset of P2 where fi(x) = x² – 3, f2(x) = x2 – 2x and f3(x) = x. Show that B is a basis of P2. (b) Determine whether or not the following sets are subspaces of F. (i) X = {f € F | f(x) = a(x + cos x), a € R}. (ii) Y = {f EF | f(x) = ax + sin x, a € R}. (c)...
11. Let the universal set be the set U = {a,b,c,d,e,f,g} and let A = {a,c,e,g}...
11. Let the universal set be the set U = {a,b,c,d,e,f,g} and let A = {a,c,e,g} and B = {d, e, f, g}. Find: A ∪ B 12. Let the universal set be the set U = {a,b,c,d,e,f,g} and let A = {a,c,e,g} and B = {d, e, f, g}. Find: b. A ∩ B 13. Let the universal set be the set U = {a,b,c,d,e,f,g} and let A = {a,c,e,g} and B = {d, e, f, g}. Find: AC...
Let fi and f2 be functions such that lim e s f1 (2) = + and...
Let fi and f2 be functions such that lim e s f1 (2) = + and such that the limit L2 = lim a s f2 (x) exists. Which one of the following is NOT correct? O limas (f1f2)(x) = 0 if L2 = 0. limas (fi + f2)(x) = too if L2 = -0. Olim as (f1f2) (x) = too if 0 <L2 5+co. lim a s (f1f2)(x) = - it L2 = -. Which one of the following...
Question 2 {(1,-,,,1)} and C {(1,-,0), 0, 0,1)} be subsets of R3 Let B (a) Show...
Question 2 {(1,-,,,1)} and C {(1,-,0), 0, 0,1)} be subsets of R3 Let B (a) Show that both the sets B and C are lhnearly independent sets of vectors with spanB = spanC 12 marks (b) Assuming the usual left to rıght orderıng, find the transıtion matrıx PB-C [2 marks (c) Given a basıs D of R, find the transıtion matrıx PBD given 2 1 3 2 Pc-D 3 marks (c) to find D (d) Use the transıtion matrıx PcD...
Let M be a ơ-algebra of subsets of X and P the set of finite measures on M. Prove that (a) d(μ, v) = supAEM |μ( A)-v(A)| defines a metric on P (b) (P, d) is complete.
Let M be a ơ-algebra of subsets of X and P the set of finite measures on M. Prove that (a) d(μ, v) = supAEM |μ( A)-v(A)| defines a metric on P (b) (P, d) is complete.
Three forces acting on an object are given by F1 = (-1.551+ 5.70j N, F2 4.55-1.8j) N, and F3 -42i) N. The object experiences an acceleration of magnitude 3.85 m/s2 (a) What is the direction of the acceleration? (counterclockwise from the +x-axis) (b) What is the mass of the object? kg (c) If the object is initially at rest, what is its speed after 19.0 s? m/s (d) What are the velocity components of the object after 19.0 s? (Let...
(a) State what is meant by saying that F is a σ-field on a set Ω. I. (b) Let F1 and F2 be two-fields on a set Ω. Is Ћ UF2 a-field on Ω? If yes, show that Fİ UF2 is a σ-field on Ω. If not, give a counterexample. , isaơ-field on . (c) Let 2-11,2,3,4,5,6,7,8,9,10) and F(A) be the o-field generated by A - 11,2,3,5, 10), 2,8,51, 16,7)1 (i) Find F(A); (ii) Give an example of four-fields F1,...
2. Given the set S-ta,b,c,d,e,f,g,h) a) How many subsets does S have? b) How many subsets have exactly 5 elements? c) A subset is randomly chosen for the collection of all possible a) b) c) subsets. What is the probability that it contains exactly 3 elements? d) A subset is chosen at random from all the subsets. d) What is the probability that it contains the element a?
2. Let A and B be subsets of a sample space S. The relative complement of B with respect to A is denoted and give by A B(r:r E A and r (a) Express B as a relative complement. (b) Prove that A B An B. (c) Prove that (A\B) A*UB. (d) Prove that p(AP)-P(1)-P(An B). B).
Let S be the universal set, where: S = {1, 2, 3, ..., 18, 19, 20} Let sets A and B be subsets of S, where: Set A = {2,5, 6, 7, 8, 14, 18} Set B = {1, 2, 3, 4, 7, 9, 10, 11, 12, 14, 18, 19, 20} Find the following: The cardinality of the set (A U B): n(AUB) = The cardinality of the set (A n B): n(An B) is You may want to draw...
2. (a) Let B = {f1, f2, f3} be a subset of P2 where fi(x) = x² – 3, f2(x) = x2 – 2x and f3(x) = x. Show that B is a basis of P2. (b) Determine whether or not the following sets are subspaces of F. (i) X = {f € F | f(x) = a(x + cos x), a € R}. (ii) Y = {f EF | f(x) = ax + sin x, a € R}. (c)...
Let fi and f2 be functions such that lim e s f1 (2) = + and such that the limit L2 = lim a s f2 (x) exists. Which one of the following is NOT correct? O limas (f1f2)(x) = 0 if L2 = 0. limas (fi + f2)(x) = too if L2 = -0. Olim as (f1f2) (x) = too if 0 <L2 5+co. lim a s (f1f2)(x) = - it L2 = -. Which one of the following...
Question 2 {(1,-,,,1)} and C {(1,-,0), 0, 0,1)} be subsets of R3 Let B (a) Show that both the sets B and C are lhnearly independent sets of vectors with spanB = spanC 12 marks (b) Assuming the usual left to rıght orderıng, find the transıtion matrıx PB-C [2 marks (c) Given a basıs D of R, find the transıtion matrıx PBD given 2 1 3 2 Pc-D 3 marks (c) to find D (d) Use the transıtion matrıx PcD...
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