1   My opinion of Matlab

(copied from class 9).

1. Advantages
   1. Excellent quality numerical routines.
   2. Free at RPI.
   3. Many toolkits available.
   4. Uses parallel computers and GPUs.
   5. Interactive - you type commands and immediately see results.
   6. No need to compile programs.
2. Disadvantages
   1. Very expensive outside RPI.
   2. Once you start using Matlab, you can't easily move away when their prices rise.
   3. You must force your data structures to look like arrays.
   4. Long programs must still be developed offline.
   5. Hard to write in Matlab's style.
   6. Programs are hard to read.
3. Alternatives
   1. Free clones like Octave are not very good
   2. The excellent math routines in Matlab are also available free in C++ librarues
   3. With C++ libraries using template metaprogramming, your code looks like Matlab.
   4. They compile slowly.
   5. Error messages are inscrutable.
   6. Executables run very quickly.

2   Homework grading rules

1. Each homework grade will be normalized to be out of 100.
2. Then the lowest homework grade will be dropped.
3. There will be only 9 homeworks.

3   Useful tables in book

1. TABLE 3.1 Discrete random variables is page 115.
2. TABLE 4.1 Continuous random variables is page 164.

4   Worked out problems from book

1. 5.30, page 263
2. 5.33, p 267

5   Review questions

1. What is $$\int_{-\infty}^\infty e^{\big(-\frac{x^2}{2}\big)} dx$$?

   1. 1/2
   2. 1
   3. $2\pi$
   4. $\sqrt{2\pi}$
   5. $1/\sqrt{2\pi}$

2. What is the largest possible value for a correlation coefficient?

   1. 1/2
   2. 1
   3. $2\pi$
   4. $\sqrt{2\pi}$
   5. $1/\sqrt{2\pi}$

3. The most reasonable probability distribution for the number of defects on an integrated circuit caused by dust particles, cosmic rays, etc, is

   1. Exponential
   2. Poisson
   3. Normal
   4. Uniform
   5. Binomial

4. The most reasonable probability distribution for the time until the next request hits your web server is:

   1. Exponential
   2. Poisson
   3. Normal
   4. Uniform
   5. Binomial

5. If you add two independent normal random variables, each with variance 10, what is the variance of the sum?

   1. 1
   2. $\sqrt2$
   3. 10
   4. $10\sqrt2$
   5. 20

6. X and Y are two uniform r.v. on the interval [0,1]. X and Y are independent. Z=X+Y. What is E[Z]?

   1. 0
   2. 1/2
   3. 2/3

7. Now let W=max(X,Y). What is E[W]?

   1. 0
   2. 1/2
   3. 2/3

8. Experiment: toss two fair coins, one after the other. Observe two random variables:

   1. X is the number of heads.
   2. Y is the toss when the first head occurred, with 0 meaning both coins were tails.

   What is P[X=1]?

   1. 0
   2. 1/4
   3. 1/2
   4. 3/4
   5. 1

9. What is P[Y=1]?

   1. 0
   2. 1/4
   3. 1/2
   4. 3/4
   5. 1

10. What is P[Y=1 & X=1]?

    1. 0
    2. 1/4
    3. 1/2
    4. 3/4
    5. 1

11. What is P[Y=1|X=1]?

    1. 0
    2. 1/4
    3. 1/2
    4. 3/4
    5. 1

12. What is P[X=1|Y=1]?

    1. 0
    2. 1/4
    3. 1/2
    4. 3/4
    5. 1

13. These next few questions concern math SAT scores, which we assume have a mean of 500 and standard deviation of 100.

    What is the probability that one particular score is between 400 and 600?

    1. .34
    2. .68
    3. .96
    4. .98
    5. .9974

14. I take a random sample of 4 students, and compute the mean of their 4 scores. What is the probability that that mean is between 400 and 600?

    1. .34
    2. .68
    3. .96
    4. .98
    5. .9974

15. I take a random sample of 9 students, and compute the mean of their 9 scores. What is the probability that that mean is between 400 and 600?

    1. .34
    2. .68
    3. .96
    4. .98
    5. .9974

16. What is the standard deviation of the 4-student sample?

    1. 25
    2. 33
    3. 50
    4. 100
    5. 200

17. What is the standard deviation of the 9-student sample?

    1. 25
    2. 33
    3. 50
    4. 100
    5. 200