In this problem we outline a proof of Theorem 7.4.3 in the case n = 2. Let x(1) and x(2) be solutions of equation (3) for < t < , and let W be the Wronskian of x(1) and x(2) . a. Show that dW dt = ________ dx(1) 1 dt dx(2) 1 dt x(1) 2 x(2) 2 ________ + ________ x(1) 1 x(2) 1 dx(1) 2 dt dx(2) 2 dt ________ . b. Using equation (3), show that dW dt = ( p11 + p22)W. c. Find W(t) by solving the differential equation obtained in part b. Use this expression to obtain the conclusion stated in Theorem 7.4.3. d. Prove Theorem 7.4.3 for an arbitrary value of n by generalizing the procedure of parts a, b, and c.

Chapter 1: Basic Ideas 1.1: Sampling Lecture Notes 1/9/17 STATISTICS → math discipline; study of procedures for collecting and describing data and drawing conclusions from the obtained information POPULATION vs SAMPLE → population: entire set of individuals → sample: subset of population SIMPLE RANDOM SAMPLE (SRS) → sample chosen by a method where each collection...