Okay, here is a list of homework that has been assigned during the term. Starting with the assignment given on 2/23.

• (Previously assigned. 1-R1,2-R2,2-R3,2-R11,2-R13.
  

• Assigned 2/23. Due 3/2.
  2.38, 2-R11, 5.52, 5.53
  

  a) Figure out the rest of the “parallel axis theorem”

  $$E( (X - c)^2) - var(X) + \dots$$

  b) Suppose $E(X_i) = \mu_i$ and $var(X_i) = \sigma_i^2$ for $i = 1,2$. Futhermore, assume $X_1,X_2$ are independent. Find the following

  • $E(xX_1 + b)$

  • $var(aX_1_b)$

  • $E(X_1 - X_2)$ (Did you use independence?)

  • $var(X_1 - X_2)$ (Did you use independence?)

• Assigned 2/25. Due 3/4. Here are two math questions.
  

  a) Show that the mean average deviation is always less or equal to the standard deviation.
  

  (Hint. Show first that for any random variable $X$ that $var(X) = E((X-E(X))^2) = E(X^2) - (E(X))^2 \geq 0$.)

  b) SHow that the Cauchy distribution ($f(x) = \pi^{-1}(1+x^2)^{-1}$) describes the position of $x$ in the drawing when $t$ is assumed uniform on $[-\pi/2,\pi/2]$.
  

  (Hint. Use trigonometry to find an equation between $x$ and $t$ and then compute $F_x(z) = P(x \leq z)$ and show this is the same as that for the Cauchy which is $F(z) = \int f(x) dx = \pi^{-1}(arctan(z) + \pi/2)$.)

• Homework for Sections 8.2:
  8.3: 8.3, 8.7, 8.9, 8.13

• Homework for Sections 8.5-8.10
  8-22, 2-27, 8-35, 8-37.

• We skip (for now) the sections on Bayesian statistics (8.11-8.13).

• Homework for 9.1,9.2: (Assigned 3/23)
  9-1, 9-2, 9-4, 9-8

• Homework for 9.3,9.4: (Assigned 3/25)
  9-14, 9-20

• Homework for 9.5-9.7: (Assigned 3/25)
  9-24,9-26,9-28

• Homework for Ch 10: 10.3, 10.5, 10.8, 10-10, 10-14, 10-19.

• Homework for ch 12: 12-2 12-9 12-10. This is on 2 sample tests

• Homework for ch 13: 13-1 13-5 13-18 13-19. This is on the $\chi^2$ test for fit and independence.

So far that’s it. You should be expecting 3 to 4 problems per class period. I’m keeping this relatively small, with the idea that you will do of them.