Stat 2000, Section 001, Homework Assignment 12 (Due 11/29/2001 11:59pm)
- 0) Reading: Section 5.1, 5.2
- 1) Please work on the following textbook questions in Moore/McCabe:
- a) Exercise 5.1, 5.2, 5.4, 5.6, 5.11, 5.12 (1 Point each)
- b) Exercise 5.18, 5.20, 5.21 (2 Points each)
- c) Exercise 5.24, 5.26, 5.30, 5.34 (1 Point each)
- 2) Recall the bahavior of the manipulated coin (70% chance
of head) we discussed in our 4/10/00 lecture. Suppose we toss
this coin 1000 times. (3 Points)
- a) What are mean, variance, and standard deviation for a
random variable X that is related to this coin?
- b) What is the probability to end up with 700 to 900 times
head with this coin? Use an appropriate approximation to calculate
this probability.
- c) And what is the probability to end up with 700 to 900 times
head with a "fair" coin? Use an appropriate approximation again
to calculate this probability.
- 3) Work with the Central Limit Theorem applet at
http://www.stat.sc.edu/~west/javahtml/CLT.html
Roll 3 dice once, 10 times, 50 times, 100 times, 500 times
and decribe your observations. How does this compare to
rolling 1 die the same number of times? And what
happens if you roll 5 dice the same number of times?
(3 Points)
- 4) Work with the Normal Approximation to Binomial applet at
http://www.ruf.rice.edu/~lane/stat_sim/normal_approx/index.html
Select N = 5 and set "from" = 2 and "to" = 4. Then use
p = 0.1, 0.5, and 0.8, and report what the exact binomial
probabilities and the probabilities by the normal approximation are.
Similarly, work with N = 50, "from" = 20 and "to" = 30. Use
p = 0.4, 0.5, and 0.7 here. Report the probabilities.
Finally, look at N = 500, "from" = 240, "to" = 260, and p = 0.5
and report the probabilities.
Experiment with some other parameters and
summarize your findings in two or three sentences.
(3 Points)
Happy Thanksgiving !!!