ANNOUNCEMENTS
DO NOT FORGET TO READ THE TEXTBOOK.
Test 1: October 13, 2009 in class
Why_I_Will_Never_Have_a_Girlfriend (by Tristan Miller)
How did he get 3493 weeks in the "Conclusion" ?
The homework must be handed in at the beginning of class on the Monday of the week following the posted assignement date. (Not at the discussion section as indicated in the syllabus).
Homework 1 (7 September, 2009)
1) 2.30 p48,
2) 2.11 p37,
3) 3.58 p116, hint: use complementation rule
4) 3.61a,b p116 : birthday problem
5) 3.66 p116
Homework 2 (14 September, 2009)
1) State the "good-defective" example discussed in class and make a corresponding tree diagram.
2) 4.46 p157 (Yatzee)
3) 4.48 p158 : Probability = length of the interval
4 ) 4.66 p164 : sporting goods
5) 4.74 p165 : balanced and and unbalanced coins
Homework 3 (21 September, 2009). SPECIAL: due on Friday Sept 25 in class .
1) 5.43 a,b p206 (binomial)
2) 5.45 p206 (binomial)
3) 5.50 p206 (seq of random decimal digits)
4) 5.63 p217 (hypergeometric)
5) 5.80 p226 (Poisson approx. of binomial)
Homework 4 (28 September, 2009). Due Monday Oct 5. (Homework 3 is due on Friday Sept 25)
1) 5.82 p226 (Poisson)
2) 5.94 p235 (geometric)
3) 5.117 p224 (negative binomial = pascal)
4) 6.2 p.269 (joint))
5) 6.45 p288 (joint)
Homework 5 (5 October, 2009). Due next Tuesday, October 13.
1) 6.73 P299 (hospital)
2) 6.133 p320 (hypergeometic)
3) 6.136 p320 (multinomial)
4) 7.1 p333 (binomial)
5) 7.11 p334 (sickle cell anemia)
Homework 6 (14 October, 2009). Due the following Monday.
1) 7.86 p374 (variance)
2) 7.92 p375 (correlation)
3) 7.93 p375 (multinomial)
4) 7.102 p376 (standardization)
5) 7.106 p376 ( bilinearity of the covariance)
Homework 7 (19 October, 2009).
1) 7.109 p376 (the sample variance is an unbiased estimator)
2) 7.120 p389 (random sum)
3) 8.25 p414 (cdf)
4) 8.27 p414 + compute PDF
5) 8.30 p415 (given PDF)
Homework 8 (26 October, 2009). [Long: start early]
1) 8.49 p426 (given PDF)
2) 8.33 p415 and also 8.80 p436
Hint: for the min, start with P(X>x) and ask yourself what {X>x} implies about X_1,...,X_m. Then use independence.
Hint: for the max, start with P(X<=x) and ask yourself what {X<=x} implies about X_1,...,X_m. Then use independence.
3) 8.101 p448 (normal; b: conditional probability)
4) 8.105 p449 (transformation: use CDF method)
5)8.154 p474 (lognormal) (transformation: use PDF method)
Homework 9 (2 November, 2009).
1) 8.160 p474 (transformation: use PDF method): chi-squared distribution defined on P456
2) 8.164 p475 (simulation: indicate how you simulated your Unif(0,1)). You can search on the web for a random number generator for windows, or, better, use MATLAB and type random('unif',0,1). For Part c, provide a graph of the empirical CDF.
3) You want to simulate three values of a standard normal random variable. Suppose you have generated the values 0.9838, 0.5, 0.0616 of a uniform on (0,1). What are the three corresponding values of the standard normal random variables (Hint: use cdf table on page A.39). Explain your method.
4) 9.26 p500: (pdf + cdf)
5) 9.45 p507 P(X>Y): integrate over the region x>y
Homework 10 (9 November, 2009).
1) 9.64c p519: determine first the conditional density
2) 9.77 p521: show non-negative and integrates to 1
3) 9.91 p528: independence ('at random' = uniform)
4) 9.122, p543: convolution
5) 10.82a,b p605: conditional expectation
Homework 11 (16 November, 2009).
1) 9.126, p543 (normal)
2) 11.2 p639: (MGF Poisson)
3) 11.55a,c p672: (Binomial -> CLT)
4) 11.57, p672 (CLT) roulette. "Ahead" means T_n = number of wins > n/2
5) 11.63 p673: (CLT)
Homework 12 (23 November, 2009). Due Wednesday December 2.
1) 11.59, p672 (CLT) batteries. Continuity correction.
2) 11.61, p673 (CLT) incomes
3) 11.91, p679 (CLT) genetics
4) 11.95 p680 (CLT) test scores
5) 11.98 p680 (CLT) (a) leave it as a sum; (b) no need for continuity correction because n is very large.