Question

In: Advanced Math

Prove that the set of classifiers F={f : f(x)=sign(sin(ωx)), ω≥0} operating in one dimension with input...

Prove that the set of classifiers F={f : f(x)=sign(sin(ωx)), ω≥0} operating in one dimension with input space X=[0,2π] is infinite.

Please write as clear as possible, the picture is always blurry, so please make sure the text is easy to read, thank you very much!

Solutions

Expert Solution


Related Solutions

a. Prove that y=sin(x) is a subspace of R^2 b. Prove that a set of 2x2...
a. Prove that y=sin(x) is a subspace of R^2 b. Prove that a set of 2x2 non invertible matrices a subspace of all 2x2 matrices
Prove that {f(x) ∈ F(R, R) : f(0) = 0} is a subspace of F(R, R)....
Prove that {f(x) ∈ F(R, R) : f(0) = 0} is a subspace of F(R, R). Explain why {f(x) : f(0) = 1} is not.
Let f(x; θ) = θxθ−1 for 0 < x < 1 and θ ∈ Ω =...
Let f(x; θ) = θxθ−1 for 0 < x < 1 and θ ∈ Ω = {θ : 0 < θ < ∞}. Let X1, . . . , Xn denote a random sample of size n from this distribution. (a) Sketch the pdf of X for (i) θ = 1/2, (ii) θ = 1 and (iii) θ = 2. (b) Show that ˆθ = −n/ ln (Qn i=1 Xi) is the maximum likelihood estimator of θ. (c) Determine the...
Given f(x,y) = 2 ; 0< x ≤ y < 1 a. Prove that f(x,y) is...
Given f(x,y) = 2 ; 0< x ≤ y < 1 a. Prove that f(x,y) is a joint pdf. b. Find the correlation coefficient of X and Y.
(a) Find the Riemann sum for f(x) = 4 sin(x), 0 ≤ x ≤ 3π/2, with...
(a) Find the Riemann sum for f(x) = 4 sin(x), 0 ≤ x ≤ 3π/2, with six terms, taking the sample points to be right endpoints. (Round your answers to six decimal places.) R6 = (b) Repeat part (a) with midpoints as the sample points. M6 = If m ≤ f(x) ≤ M for a ≤ x ≤ b, where m is the absolute minimum and M is the absolute maximum of f on the interval [a, b], then m(b...
2.a Use Rolle's Theorem to prove that if f ′ ( x ) = 0 for...
2.a Use Rolle's Theorem to prove that if f ′ ( x ) = 0 for all xin an interval ( a , b ), then f is constant on ( a , b ). b True or False. The product of two increasing functions is increasing. Clarify your answer. c Find the point on the graph of f ( x ) = 4 − x 2 that is closest to the point ( 0 , 1 ).
Prove that: a) |sinx|<= |x| b) x = sin x has only one solution in real...
Prove that: a) |sinx|<= |x| b) x = sin x has only one solution in real number using mean value theorem
The graph of f(x) = sin(2x)/x is shown in Figure 20. Is the function f(x) continuous at x = 0? Why or why not?
The graph of f(x) = sin(2x)/x is shown in Figure 20. Is the function f(x) continuous at x = 0? Why or why not?
TOPOLOGY Let f : X → Y be a function. Prove that f is one-to-one and...
TOPOLOGY Let f : X → Y be a function. Prove that f is one-to-one and onto if and only if f[A^c] = (f[A])^c for every subset A of X. (prove both directions)
Consider the function on the interval (0, 2π). f(x) = sin(x) cos(x) + 2 (a) Find...
Consider the function on the interval (0, 2π). f(x) = sin(x) cos(x) + 2 (a) Find the open interval(s) on which the function is increasing or decreasing. (Enter your answers using interval notation.) increasing     ( )    decreasing     ( )   (b) Apply the First Derivative Test to identify all relative extrema. relative maxima     (x, y) =    (smaller x-value) (x, y) = ( )    (larger x-value) relative minima (x, y) =    (smaller x-value) (x, y) = ​   ...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT