Median and Mean examples

For each type of measure, give two examples of populations where it would be the most appropriate indication of central tendency. Each type of measure is for mean, and the median.

Trouble with Bolzano-Weierstrauss

This involves the Bolzano-Weierstrauss Theorem, I believe, but I'm not sure where to start. Prove that the set of open disks in the xy plane with cneter (x,x) and radius x > 0, x rational, is a countable covering of the set {(x,y): x > 0, y > 0}

Interpolate

(See attached file for full problem description with proper equations) --- 1. For medical purposes the level of sugar was measured in blood (in mg/dl). The samples were taken with 1/2 hour increments, as the following table shows: Initial sample 96 mg/dl After 30 min. 133 mg/dl After 60 min. 142 mg/dl After 90 min. ...continues

For medical purposes the level of sugar...

(See attached file for full problem description) --- For medical purposes the level of sugar was measured in blood (in mg/dl)... ---

Legrende polynomials

(See attached file for full problem description)

Suppose that N(h) is an approximation to M for every h > 0 and...

(See attached file for full problem description with proper equations and exponents) --- 1. Suppose that N(h) is an approximation to M for every h > 0 and that M = N(h)+K1h2+K2h4+K3h6+….. For some value K1, K2, K3… Use the values N(h), N(h/3), and N(h/9) to produce an O(h6) approximation to M. ---

Approximate the integrals using the Trapezoidal rule.

(See attached file for full problem description with proper equations and exponents) --- 1. Approximate the integrals using the Trapezoidal rule. a) Integral from -0.5 to 0 x ln(x+1) dx b) Integral from 0.75 to 1.3 ((sin x)2 - 2x sin x +1) dx 2. Find a bound for error in question 1. using the error formula, and comp ...continues

1. The trapezoid rule applied to the integral from 0 to 2 f(x) dx gives the value 5, and the midpoint rule gives the value 4. What value does Simpson's rule give?

1. The trapezoid rule applied to the integral from 0 to 2 f(x) dx gives the value 5, and the midpoint rule gives the value 4. What value does Simpson's rule give?

Fixed Point Iteration Problem

(See attached file for full problem description with proper symbols) --- Given the function , show that it has a unique fixed point in the interval and that the iterations converge to the fixed point for any . Also, find the number of iterations necessary to guarantee that . Write a short Matlab code to find t ...continues

Proving an Inequality

(See attached file for full problem description with equation and symbols) --- Let be an increasing sequence of positive real numbers. Prove that Can anything be said about the constant 4? ---