1 Grade

1. There will be no homework assigned today. Homework 21, due today, was the last.

2. Per the syllabus, the lowest of your 3 exam grades will be dropped.

3. In a day or so, I will calculate your guaranteed grade if you don't write the final, and try to post it on LMS.

4. If you write the final, it can only raise your grade.

5. In a few days, I might post a survey to see if anyone at all wants to write the final.

6. In particular if you're in China and want to write the final 12 hours later, then write me. Only people now physically in east Asia or similar places are allowed to do this.

2 No video for class 25

Something didn't work.

(The 25 is a correction; earlier I said 24.)

3 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

Time, number, title
7:41, 73, Generating Samples of a Random Variable
8:18, 74, Tips and Tricks for Random Number Generation