![/ 4Given p > 1, find a function f such that l e L(0,1) for <p but fe L(0,1]) for s p. Find another function g such that ge](http://img.homeworklib.com/questions/5cfc2d40-ac6d-11eb-b0d0-8f793f3a7365.png?x-oss-process=image/resize,w_560)
Homework Answers
7. (10%) Let f: [0,1] R be defined by _x xe[0,1]n f(x) 0 otherwise Is fe L[0,1]? If yes, find its Lebesgue integral...
7. (10%) Let f: [0,1] R be defined by _x xe[0,1]n f(x) 0 otherwise Is fe L[0,1]? If yes, find its Lebesgue integral. i) Is feR[O,1] ? If yes, find its Riemann integral. ii) ii) What is lim || |, ?
7. (10%) Let f: [0,1] R be defined by _x xe[0,1]n f(x) 0 otherwise Is fe L[0,1]? If yes, find its Lebesgue integral. i) Is feR[O,1] ? If yes, find its Riemann integral. ii) ii) What is lim ||...
Probability and measure Consider (21,F,P)-((0,1), B, A) and measurable function p: (0,1)R given by p(t)4t (1...
Probability and measure
Consider (21,F,P)-((0,1), B, A) and measurable function p: (0,1)R given by p(t)4t (1 t). Find the CDF for the measure induced by p on (R, B)
real analysis II. Consider the function f:[0,1] - R defined by f(x) 0 if x E...
real analysis
II. Consider the function f:[0,1] - R defined by f(x) 0 if x E [0,1]\ Q and f(x) = 1/q if x = p/q in lowest terms. 1. Prove that f is discontinuous at every x E Qn [0,1]. 2. Prove that f is continuous at every x e [0,1] \ Q.
II. Consider the function f:[0,1] - R defined by f(x) 0 if x E [0,1]\ Q and f(x) = 1/q if x = p/q in lowest...
(5) Let f: [0, 1 R. We say that f is Hölder continuous of order a e (0,1) if \f(x) -- f(y)| . , y sup [0, 1] with 2 # 1...
(5) Let f: [0, 1 R. We say that f is Hölder continuous of order a e (0,1) if \f(x) -- f(y)| . , y sup [0, 1] with 2 # 1£l\c° sup is finite. We define Co ((0, 1]) f: [0, 1] -R: f is Hölder continuous of order a}. = (a) For f,gE C ([0, 1]) define da(f,g) = ||f-9||c«. Prove that da is a well-defined metric Ca((0, 1) (b) Prove that (C ([0, 1]), da) is complete...
Question l: Consider the function f(x) = sin(parcsinx),-1 < x < 1 and p E R (a) Calculate f(0) in terms of p. Simplify your answer completely fX) sin(p arcsinx) f(o) P The function fand it...
Question l: Consider the function f(x) = sin(parcsinx),-1 < x < 1 and p E R (a) Calculate f(0) in terms of p. Simplify your answer completely fX) sin(p arcsinx) f(o) P The function fand its derivatives satisfy the equation where f(x) denotes the rth derivative of f(x) and f (b) Show thatf0(n2p2)f(m)(o) (x) is f(x). (nt2) (nti) (I-x) (nt 2 e 0 (c) For p E R-仕1, ±3), find the MacLaurin Series for f(x), up to and including the...
Let p E [0,1] with pメ, and let (Xn)n=o b l e the Markov chain on with initia [0,1] given by distribution δο and transi...
Let p E [0,1] with pメ, and let (Xn)n=o b l e the Markov chain on with initia [0,1] given by distribution δο and transition matrix 11: Z Z ify=x-1 p 0 otherwise. Use the strong law of large numbers to show that each state is transient. Hint: consider another Markov chain with additional structure but with the same distribution and transition matrix
Let p E [0,1] with pメ, and let (Xn)n=o b l e the Markov chain on with...
Let X ~ Unif(0,1). Find a function of X that has CDF F(x) = 1 ̶ x ̶ p for p > 0 (this is the P...
Let X ~ Unif(0,1). Find a function of X that has CDF F(x) = 1 ̶ x ̶ p for p > 0 (this is the Pareto distribution).
Suppose f is a continuous and differentiable function on [0,1] and f(0)= f(1). Let a E...
Suppose f is a continuous and differentiable function on [0,1] and f(0)= f(1). Let a E (0, 1). Suppose Vr,y(0,1) IF f'(x) 0 and f'(y) ±0 THEN f'(x) af'(y) Show that there is exactly f(ax) and f'(x) 0 such that f(x) one Hint: Suppose f(x) is a continuous function on [0, 1] and f(0) x € (0, 1) such that f(x) = f(ax) f(1). Let a e (0,1), there exists an
Suppose f is a continuous and differentiable function on...
Fix an integer N>1, and consider the function f:[0,1]R defined as follows: if XE[0,1] and there...
Fix an integer N>1, and consider the function f:[0,1]R defined as follows: if XE[0,1] and there is an integer n with 1<n<N such that nxez, choose n with this property as small as possible, and set f(x) := 1/n^2; otherwise set f(x):=0. Show that f is 0 integrable, and S f.
= Q 6. Let f: {0,1} + {0,1} be a function given by f(0) = 0...
= Q 6. Let f: {0,1} + {0,1} be a function given by f(0) = 0 = f(1). Find two (total) functions g: {0,1} +{0,1} and h: {0,1} +{0,1} such that fog #gof and foh= hof. Write out f and your chosen functions g and h in table form, using a single table. Only the table is required as the answer.
7. (10%) Let f: [0,1] R be defined by _x xe[0,1]n f(x) 0 otherwise Is fe L[0,1]? If yes, find its Lebesgue integral. i) Is feR[O,1] ? If yes, find its Riemann integral. ii) ii) What is lim || |, ?
7. (10%) Let f: [0,1] R be defined by _x xe[0,1]n f(x) 0 otherwise Is fe L[0,1]? If yes, find its Lebesgue integral. i) Is feR[O,1] ? If yes, find its Riemann integral. ii) ii) What is lim ||...
Probability and measure
Consider (21,F,P)-((0,1), B, A) and measurable function p: (0,1)R given by p(t)4t (1 t). Find the CDF for the measure induced by p on (R, B)
real analysis
II. Consider the function f:[0,1] - R defined by f(x) 0 if x E [0,1]\ Q and f(x) = 1/q if x = p/q in lowest terms. 1. Prove that f is discontinuous at every x E Qn [0,1]. 2. Prove that f is continuous at every x e [0,1] \ Q.
II. Consider the function f:[0,1] - R defined by f(x) 0 if x E [0,1]\ Q and f(x) = 1/q if x = p/q in lowest...
(5) Let f: [0, 1 R. We say that f is Hölder continuous of order a e (0,1) if \f(x) -- f(y)| . , y sup [0, 1] with 2 # 1£l\c° sup is finite. We define Co ((0, 1]) f: [0, 1] -R: f is Hölder continuous of order a}. = (a) For f,gE C ([0, 1]) define da(f,g) = ||f-9||c«. Prove that da is a well-defined metric Ca((0, 1) (b) Prove that (C ([0, 1]), da) is complete...
Question l: Consider the function f(x) = sin(parcsinx),-1 < x < 1 and p E R (a) Calculate f(0) in terms of p. Simplify your answer completely fX) sin(p arcsinx) f(o) P The function fand its derivatives satisfy the equation where f(x) denotes the rth derivative of f(x) and f (b) Show thatf0(n2p2)f(m)(o) (x) is f(x). (nt2) (nti) (I-x) (nt 2 e 0 (c) For p E R-仕1, ±3), find the MacLaurin Series for f(x), up to and including the...
Let p E [0,1] with pメ, and let (Xn)n=o b l e the Markov chain on with initia [0,1] given by distribution δο and transition matrix 11: Z Z ify=x-1 p 0 otherwise. Use the strong law of large numbers to show that each state is transient. Hint: consider another Markov chain with additional structure but with the same distribution and transition matrix
Let p E [0,1] with pメ, and let (Xn)n=o b l e the Markov chain on with...
Suppose f is a continuous and differentiable function on [0,1] and f(0)= f(1). Let a E (0, 1). Suppose Vr,y(0,1) IF f'(x) 0 and f'(y) ±0 THEN f'(x) af'(y) Show that there is exactly f(ax) and f'(x) 0 such that f(x) one Hint: Suppose f(x) is a continuous function on [0, 1] and f(0) x € (0, 1) such that f(x) = f(ax) f(1). Let a e (0,1), there exists an
Suppose f is a continuous and differentiable function on...
Fix an integer N>1, and consider the function f:[0,1]R defined as follows: if XE[0,1] and there is an integer n with 1<n<N such that nxez, choose n with this property as small as possible, and set f(x) := 1/n^2; otherwise set f(x):=0. Show that f is 0 integrable, and S f.
= Q 6. Let f: {0,1} + {0,1} be a function given by f(0) = 0 = f(1). Find two (total) functions g: {0,1} +{0,1} and h: {0,1} +{0,1} such that fog #gof and foh= hof. Write out f and your chosen functions g and h in table form, using a single table. Only the table is required as the answer.
Most questions answered within 3 hours.
-
1. Which of the following is a cost of unemployment? a.
Unemployed individuals suffer a loss...
asked 1 minute from now -
What z Score do we need in order to have a total of 1% (or less)...
asked 5 minutes ago -
Which of the following is a query that you CANNOT write in
Standard SQL over a...
asked 15 minutes ago -
If all I have is a mean concentration, how can I
calculate the overall confidence limit,...
asked 9 minutes ago -
In the lab, you prepare a solution in a 150 mL volumetric flask
by mixing 25.0...
asked 16 minutes ago -
1. Consider the reaction: 2 NO (g) + 2 H2 (g) → N2 (g) + 2...
asked 17 minutes ago -
The equilibrium constant for the dissociation of trichloroacetic
acid at STP is 1.995 x 10^-1. What...
asked 24 minutes ago -
An ideal gas is confined to a container with constant volume.
The number of moles is...
asked 33 minutes ago -
FIVE-PART PROBLEM: The visible spectrum of colors ranges
from approximately 380 nm in wavelength at the...
asked 35 minutes ago -
Brooke and Georgia are neighbors. Each have 40 hours per week.
Brooke needs 5 hours to...
asked 1 hour ago -
Quantitative Problem: You are holding a
portfolio with the following investments and betas:
Stock
Dollar investment...
asked 1 hour ago -
Within the costing system of a manufacturing company the
following types of expenses were incurred:
Details...
asked 1 hour ago