![Exercise 6.8. Recall the geometric description of the Cantor set. With Ko:-[0, 1], we constructed i Go(o) UG2(o). With d) the](http://img.homeworklib.com/images/0bc98826-aff2-4bad-81cc-0621214fcea2.png?x-oss-process=image/resize,w_560)
Homework Answers
You didn't mention what distance defined in (2) so I have taken it as Euclidean distance of it is something else please let me know in comment box .
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Exercise 6.8. Recall the geometric description of the Cantor set. With Ko:-[0, 1], we constructed...
Consider the construction of the Cantor set C c [0, 1] In the st step we...
Consider the construction of the Cantor set C c [0, 1] In the st step we remove the open interval (, ) ad are left with two closed intervals [0· and [릎,1]. Let J1 denote one of these two closed intervals. In the 2nd step, we divide J into three intervals and remove the open middle third interval. We are left with two closed intervals inside J. Let J2 denote one of these two intervals. For example, if Ji were...
Problem set 9 (10 marks). Let K be a KC UFENI The aim of this exercise is to prove that there is n finite union of...
Problem set 9 (10 marks). Let K be a KC UFENI The aim of this exercise is to prove that there is n finite union of the open intervals) compact set of R and (I,)rEN be open intervals such that N such that K C I U..U (i.e. K is actually contained in a n E N, select a, K such that 1. Assume that the result does not hold, and explain why we can then, for any n UUIn...
So we are using the PhET Geometric Optics simulation to complete these problems. I'm lost on...
So we are using the PhET Geometric Optics simulation to complete
these problems. I'm lost on how to find the focal distance that we
use for table 1, and I don't know what formulas to use for the
table either.
Set the len's refractive index (n) to 1.8 and the radius
curvature (R) to .7 m. find the focal distance (f).
Using the focal distance you just found, complete the table.
Repeat the previous exercise, but with a very different...
Give a geometric description of the set of points whose coordinates satisfy the given conditions. 1)...
Give a geometric description of the set of points whose coordinates satisfy the given conditions. 1) X-5-4 A) All points in the x-z plane B) The line through the point (5.0,-4) and parallel to the y-axis C) The line through the point (5. -4,0) and parallel to the z-axis D) The point (5.-4) Describe the given set of points with a single equation or with a pair of equations. 2) The plane perpendicular to the y-axis and passing through the...
5. Consider the sample space Ω = [0, 1]. Let P be a probability function such...
5. Consider the sample space Ω = [0, 1]. Let P be a probability function such that for any interval fa, b, P(a, b-b-a. In other words, probabilty of any interval is its length Let us start with Co [0, 1, and at nth step, we define Cn by removing an interval of length 1/3 from the middle of each interval in Cn-1 For example, C1-[0, 1/3 u [2/3,1], C2-[0,1/9)U[2/9,1/3 U [2/3,7/9 U[8/9, 1] and so on. Here is a...
Please all thank you Exercise 25: Let f 0,R be defined by f(x)-1/n, m, with m,nENand n is the minimal n such that m/n a) Show that L(f, P)0 for all partitions P of [0, 1] b) Let mE N. Show that t...
Please all thank you
Exercise 25: Let f 0,R be defined by f(x)-1/n, m, with m,nENand n is the minimal n such that m/n a) Show that L(f, P)0 for all partitions P of [0, 1] b) Let mE N. Show that the cardinality of the set A bounded by m(m1)/2. e [0, 1]: f(x) > 1/m) is c) Given m E N construct a partition P such that U(f, Pm)2/m. d) Show that f is integrable and compute Jo...
Gradient descent weight update rule for a tanh unit. (2 pts) Assume throughout this exercise that we are using gradien...
Gradient descent weight update rule for a tanh unit. (2 pts) Assume throughout this exercise that we are using gradient descent to minimize the error as defined in formula (4.2) on p.89 in the textbook: td -od Recall that the corresponding weight update rule for a sigmoid unit like the one in Figure 4.6 on p.96 in the textbook is: td - od) od (1-od) i,d ded Let us replace the sigmoid function σ in Figure 4.6 by the function...
Sets, Please respond ASAP, Thank you 2) Recall another notation for the natural numbers, N, is...
Sets,
Please respond ASAP,
Thank you
2)
Recall another notation for the natural numbers, N, is Z+. We similarly define the negative integers by: 2. Too, for any set A and a e R, define: and Let B={x: x E Z+ & x is odd } (Recall a number I is said to be odd if 2k +1 for some k e z) Assume Z is our underlying background set for this problem. (a) Write an expression for 3 +...
Exercise 1 Use Top-Down Design to “design” a set of instructions to write an algorithm for...
Exercise 1 Use Top-Down Design to “design” a set of instructions to write an algorithm for “travel arrangement”. For example, at a high level of abstraction, the algorithm for “travel arrangement” is: book a hotel buy a plane ticket rent a car Using the principle of stepwise refinement, write more detailed pseudocode for each of these three steps at a lower level of abstraction. Exercise 2 Asymptotic Complexity (3 pts) Determine the Big-O notation for the following growth functions: 1....
For observations {Y, X;}=1, recall that for the model Y = 0 + Box: +e the...
For observations {Y, X;}=1, recall that for the model Y = 0 + Box: +e the OLS estimator for {00, Bo}, the minimizer of E. (Y: - a - 3x), is . (X.-X) (Y-Y) and a-Y-3X. - (Xi - x) When the equation (1) is the true data generating process, {X}- are non-stochastic, and {e} are random variables with B (ei) = 0, B(?) = 0, and Ele;e;) = 0 for any i, j = 1,2,...,n and i j, we...
Consider the construction of the Cantor set C c [0, 1] In the st step we remove the open interval (, ) ad are left with two closed intervals [0· and [릎,1]. Let J1 denote one of these two closed intervals. In the 2nd step, we divide J into three intervals and remove the open middle third interval. We are left with two closed intervals inside J. Let J2 denote one of these two intervals. For example, if Ji were...
Problem set 9 (10 marks). Let K be a KC UFENI The aim of this exercise is to prove that there is n finite union of the open intervals) compact set of R and (I,)rEN be open intervals such that N such that K C I U..U (i.e. K is actually contained in a n E N, select a, K such that 1. Assume that the result does not hold, and explain why we can then, for any n UUIn...
So we are using the PhET Geometric Optics simulation to complete
these problems. I'm lost on how to find the focal distance that we
use for table 1, and I don't know what formulas to use for the
table either.
Set the len's refractive index (n) to 1.8 and the radius
curvature (R) to .7 m. find the focal distance (f).
Using the focal distance you just found, complete the table.
Repeat the previous exercise, but with a very different...
Give a geometric description of the set of points whose coordinates satisfy the given conditions. 1) X-5-4 A) All points in the x-z plane B) The line through the point (5.0,-4) and parallel to the y-axis C) The line through the point (5. -4,0) and parallel to the z-axis D) The point (5.-4) Describe the given set of points with a single equation or with a pair of equations. 2) The plane perpendicular to the y-axis and passing through the...
5. Consider the sample space Ω = [0, 1]. Let P be a probability function such that for any interval fa, b, P(a, b-b-a. In other words, probabilty of any interval is its length Let us start with Co [0, 1, and at nth step, we define Cn by removing an interval of length 1/3 from the middle of each interval in Cn-1 For example, C1-[0, 1/3 u [2/3,1], C2-[0,1/9)U[2/9,1/3 U [2/3,7/9 U[8/9, 1] and so on. Here is a...
Please all thank you
Exercise 25: Let f 0,R be defined by f(x)-1/n, m, with m,nENand n is the minimal n such that m/n a) Show that L(f, P)0 for all partitions P of [0, 1] b) Let mE N. Show that the cardinality of the set A bounded by m(m1)/2. e [0, 1]: f(x) > 1/m) is c) Given m E N construct a partition P such that U(f, Pm)2/m. d) Show that f is integrable and compute Jo...
Gradient descent weight update rule for a tanh unit. (2 pts) Assume throughout this exercise that we are using gradient descent to minimize the error as defined in formula (4.2) on p.89 in the textbook: td -od Recall that the corresponding weight update rule for a sigmoid unit like the one in Figure 4.6 on p.96 in the textbook is: td - od) od (1-od) i,d ded Let us replace the sigmoid function σ in Figure 4.6 by the function...
Sets,
Please respond ASAP,
Thank you
2)
Recall another notation for the natural numbers, N, is Z+. We similarly define the negative integers by: 2. Too, for any set A and a e R, define: and Let B={x: x E Z+ & x is odd } (Recall a number I is said to be odd if 2k +1 for some k e z) Assume Z is our underlying background set for this problem. (a) Write an expression for 3 +...
For observations {Y, X;}=1, recall that for the model Y = 0 + Box: +e the OLS estimator for {00, Bo}, the minimizer of E. (Y: - a - 3x), is . (X.-X) (Y-Y) and a-Y-3X. - (Xi - x) When the equation (1) is the true data generating process, {X}- are non-stochastic, and {e} are random variables with B (ei) = 0, B(?) = 0, and Ele;e;) = 0 for any i, j = 1,2,...,n and i j, we...
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