Let N = {1,.,6}, Fo = P(N), and P(-) be such that P({i}) = ¿. Let F = o({1,2}, {3,4}, {5,6}) and X({i}) = i². Using the definition of conditional expectation find E[X | F].

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Q: [3] Consider the model of aggregating private signals. suppose that we model the private information…

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Q: Let S = {a, b, c, d, e, f} with P(a) = 0.16, P(b) = 0.14, P(c) = 0.15, P(d) = 0.25, P(e) = 0.18, and…

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Q: Let A = {1,2,3,4, 5, 6} and let f:A → A be given by f(x) ={ 5 fx +1 if x± 6 if x = 6 a. Find f(6),…

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Q: X = {p, q, r, s} Y = {4, 5, 6, 7, 8} The function f: X → Y is defined as: f = {(s, 8), (r, 8), (q,…

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Q: 2. Let f: ZxZ-ZxZ be defined by f(m, n) = (3m+n,n²) a. Is fone-to-one? b. Is fonto?

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Q: Let X and Y denote the sets containing 2 and 20 distinct objects respectively and F denote the set…

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Q: 2. Use a table to express the values of each of these Boolean function. F(x, y, z) = x+yz

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Q: Let A = (1, 2, 3, 4, 5) and B = {a, b, c) and f = {(1, a), (2, a), (3, b), (4, b). (5, b)}. Choose…

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Q: Given a p.m.f. of x as below: (e-33x f(x) x = 0, 1, 2, ... = x! 0 O. W and y = 2x, then the p.m.f.…

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Q: Derive recurrence relation 24,Cx)=スJ(x)+ x Jyni (x). Jy-i (x).

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Q: Use the fum tiom to find the imoge of v and Hhe pieimuge of w. T(V.,N.) - (v, + V» , V, ), v• (3, -…

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Q: X = { 2,5,8,10}y and T= { 0, X, {5},{5,103} and T₁ = { 0, x₁ {2}, {5}, {2.5} let E1 = {2,83 and [2=…

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Q: 3. Let h: Z→ Z be the function h(r) = = x mod 4. Find h-¹(0), h-¹({0, 1, 2, 3}), and h-¹(4). Explain…

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Q: (1.2.7)List all elements in the following sets. (a) T = {m € Z | m = 1 + (−1)¹ for some integer i}…

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Q: Let A, BCR x R defined by A= {{n,m)|n, m € N, 0 < 2m(n + 1) – 3 < 5}, and B = {(1,1), (1,2), (2, 1),…

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Q: 2. Let A = {0,1, 2, 4, 5, 7} and B = {2,3, 4, 5, 8} be subsets of the set %3D %3D U = {n € Z | 0 < n…

A: Given: A=0,1,2,4,5,7  &amp; B=2,3,4,5,8 is subset of U=n∈ℤ  0≤n≤9 i.e.U=0,1,2,3,4,5,6,7,8,9 To Find…

Q: Let SF(n) be the squarefree function of n. Hence, SF(1) = 1 and SF(p¹p2²...pr) SF(n). P1P2...Pr.…

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Q: O O Let (X, E) be a measurable space. Let and 42 be two measures defined on X. Then 1. - 42 is a…

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Q: Let A = {1, 2, 3}, B= {4,5,6, 7} If f: A x B → N with f((a, b) = b – a , find the following. a. f…

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Q: 36) Consider the set of points in the set C: C= {(x, y) |x, y E Z, x² + |y| < 2}. %3D Suppose that…

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Q: Let E = [-5,20), be the universal set and Y =[-2,4], and Z = (0,10]be the subsets of %3D %3D Find:…

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Q: When is S \ T = T \ S for sets S, T?

A: Given that two sets S and T. The definition of S\T=a∈S,a∉T and T\S=b∈T,b∉S. Here, neither of these…

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Q: Let N = R, and F be all subsets so that A or A is countable. Also, let J0, A is countable |1, A° is…

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Q: Consider a set S={1,2,3,4,5} and P(x)=x−110, where x is a member of S. Calculate E(S).

A: It is given that P(x)=(x-1)/10.

Q: Suppose S = {1, 2, 3} T = { 1, 3, 5, 7} 28. S = {x|x & S and x & T} = 29. S = {x|x€ S or x ε T} =…

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Q: Let ECR. Prove that m*(E)= 0 implies that E is Lebesgue measurable.

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Q: Let E₁ and E2 be measurable sets (in R). (a) Use that the union of any two measurable sets is also a…

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Q: If e, is an estimator for e and

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Q: Let S = {a, b, c, d, e, f} with P(a) = 0.14, P(b) = 0.24, P(c) = 0.21, P(d) = 0.15, P(e) = 0.13, and…

A: From given we have : S = {a, b, c, d, e, f} P(a) = 0.14 P(b) = 0.24 P(c) = 0.21 P(d) = 0.15 P(e) =…

Q: Let S = {1,2,3,4}. Determine the set {A € P(S) : |A| = 2 }.

A: Let S = {1, 2, 3, 4}