Statistics 6401: Homework 4

• Read Ch4
• Problems Ch4 8, 13 (hint: use integration-by-parts), 29, 42, 43, 50 , 55, 77, 83, 89, 95, 99, 101, 102

• Exercise 1: Prove Var(X) = E[X ²] - (E[X])²

• Exercise 2: Prove E[Y] = E[E[Y|X]]

• Exercise 3: Prove Var(Y) = Var(E[Y|X]) + E[Var(Y|X)]

• Exercise 4: Using R simulate n = 500 Cauchy random values.  Plot the cumulative mean values versus the index.

• Exercise 5: Run the Group Testing R program to simulate the expected number, E[N], of tests performed in group testing when:

  a)   n = 100000, m = 10000, k = n/m, pi = 0.05, eta = 0.97, theta = 0.95 and

  b)   n = 100000, m =   5000, k = n/m, pi = 0.05, eta = 0.97, theta = 0.95