2. Harmonic Mean Suppose all n data values in a data set are positive, with 0...
Suppose all n data values in a data set are organized as yi < y2 <... < Yn. For each of the following measures of center, show that the measure of center always falls between the smallest and largest data values. Under what conditions does the measure of center exactly equal yı or yn? a) The mode. b) The midpoint. c) The median. ne mean.
please solve 2 to 6 with details
Advanced Calculus: HW 3 (1) Suppose that a E R has the following property: for all n e N, a < Prove that a<0. (2) Prove that the set of integers Z is not dense in R (3) Let A = {xeQ: >0}. Determine whether A is dense in R, and justify your answer with a proof. (4) Find the supremum of the set A= {a e Q: <5} (5) Let a >...
- The set of all 2 x 1 matrices C] where r < 0, with the usual operations in R2.
Let Rj be the set of all the positive real numbers less than 1, i.e., R1 = {x|0 < x < 1}. Prove that R1 is uncountable.
E3. Show that Σ(-1)k( ) = 0 for all positive integers n and k with 0-k-n E4. Show that (t) = Σ ( . 71 に0 k+1 k"d) for all positive integers n and k with 0 ksn
8. Letſ be a function that is continuous on (0, 2) and differentiable on (0,2). Suppose that (0)</(2) but that fisnor increasing on (0,2). Does' necessarily take on both positive and negative values on (0.2)?
We write R+ for the set of positive real numbers. For any positive real number e, we write (-6, 6) = {x a real number : -e < x <e}. Prove that the intersection of all such intervals is the set containing zero, n (-e, e) = {0} EER+
For all n E N prove that 0 <e- > < 2 k!“ (n + 1)! k=0 Hint: Think about Taylor approximations of the function e".
Use the equation 1,- Σ x for x < 1 1 - x n = 0 to expand the function in a power series with center c = 0. f(x) = 2 + 9x į n=0 Determine the interval of convergence. (Enter your answer using interval notation.) eBook -/1 Points] DETAILS ROGACALCET3 10.6.055. Find all values of x such that 9.22 2(n!) mel converges. (Enter your answer using interval notation.)
1. Trimmed Mean Assume the values in your data set are ordered so that y n 2 5. Define the trimmed mean of the data set to be 32 vn and n-4 What loss function does the trimmed mean minimize? Show that the loss function you give is actually minimized at the trimmed mean Which do you think is a better hypothesis, the mean or the trimmed r your answer the same for all data sets, or does it depend...