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a < 1. Show the series on -a, a] to onverges uniformly 25.9 (a) Let 0...
5. Let f,lr)- x *a. Show that {h} converges uniformly to 0 on [0, a] for...
5. Let f,lr)- x *a. Show that {h} converges uniformly to 0 on [0, a] for any a, 0 < a < 1. b. Does {f,) converge uniformly on [0, 1]?
let a,b > 0 . Prove that DI < Val
let a,b > 0 . Prove that
DI < Val
HW: Show that the series __, an n=0 converges whenever ſal < 1, and diverges whenever...
HW: Show that the series __, an n=0 converges whenever ſal < 1, and diverges whenever al > 0.
A) B) C) 1 Find the Laurent series for 22 +22 for 0 < 121 <...
A)
B)
C)
1 Find the Laurent series for 22 +22 for 0 < 121 < 2 Find the Laurent series for (z+2)}(3-2) for 2 – 3) > 5 1 Find the Laurent series for z2(z-i) for 1 < 12 – 11 < V2
5. Let X be uniformly distributed in [0, 1]. Given X = x, the r.v. Y...
5. Let X be uniformly distributed in [0, 1]. Given X = x, the r.v. Y is uniformly distributed in 0, x for 0<x<1 (a) Specify the joint pdf fxy(x,y) and sketch its region of support Ω XY. (b) Determine fxly(x1025). (c) Determine the probability P(X〈2Y). (d) Determine the probability P(X +Y 1)
For the series <1-1n in n +1 n=1 1. Does it converge? 2. Does it absolutely...
For the series <1-1n in n +1 n=1 1. Does it converge? 2. Does it absolutely converge? Please present your work in 1 pdf file with 2 pages (ONE subproblem per page)
8. Let X = {fe (C[0, 1], || ||00): f() = 1} and Y = {fe...
8. Let X = {fe (C[0, 1], || ||00): f() = 1} and Y = {fe (C[0, 1], || |co) : 0 <f() < 1}. Show that X is complete but Y is not complete .
) 1. Find the Laurent series of f(z) on the indicated domain. (a) -,2, on 0...
) 1. Find the Laurent series of f(z) on the indicated domain. (a) -,2, on 0 < |z-i| < 2. 1+22 222z 5 , on z 1| > 1
(4) Let f(x) (0 if x<0 (a) Show that f is differentiable at z (b) Is...
(4) Let f(x) (0 if x<0 (a) Show that f is differentiable at z (b) Is f'continuous on R? Is f continuous on R? Justify your answer.
0, P - 0 2 ) - 1. 3. Let (X, A,) be a complete measure...
0, P - 0 2 ) - 1. 3. Let (X, A,) be a complete measure space. Assume that A, B E A with (A) = (B) < . Show that if A CCCB, then CE A. 4 Let A and Rhe two collections of euheete of Y Aceume that any cot in 4 halanes
5. Let f,lr)- x *a. Show that {h} converges uniformly to 0 on [0, a] for any a, 0 < a < 1. b. Does {f,) converge uniformly on [0, 1]?
let a,b > 0 . Prove that
DI < Val
HW: Show that the series __, an n=0 converges whenever ſal < 1, and diverges whenever al > 0.
A)
B)
C)
1 Find the Laurent series for 22 +22 for 0 < 121 < 2 Find the Laurent series for (z+2)}(3-2) for 2 – 3) > 5 1 Find the Laurent series for z2(z-i) for 1 < 12 – 11 < V2
5. Let X be uniformly distributed in [0, 1]. Given X = x, the r.v. Y is uniformly distributed in 0, x for 0<x<1 (a) Specify the joint pdf fxy(x,y) and sketch its region of support Ω XY. (b) Determine fxly(x1025). (c) Determine the probability P(X〈2Y). (d) Determine the probability P(X +Y 1)
For the series <1-1n in n +1 n=1 1. Does it converge? 2. Does it absolutely converge? Please present your work in 1 pdf file with 2 pages (ONE subproblem per page)
8. Let X = {fe (C[0, 1], || ||00): f() = 1} and Y = {fe (C[0, 1], || |co) : 0 <f() < 1}. Show that X is complete but Y is not complete .
) 1. Find the Laurent series of f(z) on the indicated domain. (a) -,2, on 0 < |z-i| < 2. 1+22 222z 5 , on z 1| > 1
(4) Let f(x) (0 if x<0 (a) Show that f is differentiable at z (b) Is f'continuous on R? Is f continuous on R? Justify your answer.
0, P - 0 2 ) - 1. 3. Let (X, A,) be a complete measure space. Assume that A, B E A with (A) = (B) < . Show that if A CCCB, then CE A. 4 Let A and Rhe two collections of euheete of Y Aceume that any cot in 4 halanes
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