ANNOUNCEMENTS
DO NOT FORGET TO READ THE TEXTBOOK.
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.
Homework 1 (7 September, 2011)
1) 2.30 p48,
2) 2.11 p37,
3) 2.27 p47
4) 2.67 p75
5) 2.75 a) b) p77
Homework 2 (12 September, 2011) Hard! Start early.
1) 3.35 p107: license plates
2) 3.57 p116: cards
3) 3.58 p116, hint: use complementation rule
4) 3.61a,b p116 : birthday problem
5) 3.66 p116: TVs
Homework 3 (19 September, 2011)
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 4 (26 September, 2011)
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 5 ( 3 October, 2011).
1) 5.82 p226 (Poisson)
2) 5.94 p235 (geometric) [First hit]
3) 5.117 p244 (negative binomial = pascal) [Second hit]
4) 6.2 p.269 (joint)
5) 6.45 p288 (joint)
Homework 6 (12 October, 2011).
1) 6.73 P299 (hospital)
2) 6.133 p320 (hypergeometic)
3) 6.136 p320 (multinomial)
4) 7.1 p333 (binomial)
5) 7.11 p334 (mean, sickle cell anemia)
Homework 7 (17 October, 2011)
1) 7.36 p350 (mean)
2) 7.86 p374 (variance)
3) 7.92 p375 (correlation)
4) 7.102 p376 (standardization)
5) 7.106 p376 (bilinearity of the covariance)
Homework 8 (24 October, 2011).
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 9 (October 31, 2011).
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: involves conditional probability)
4) 8.105 p449 (transformation: use CDF method)
5)8.154 p474 (lognormal) (transformation: use PDF method)
Read: (not part of homework) Why_I_Will_Never_Have_a_Girlfriend (by Tristan Miller)
How did he get 3493 weeks in the "Conclusion" ?
Homework 10 (7 November, 2011).
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 11 (14 November, 2011).
Four problems only
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) 9.150 p551 (bivariate transformation)
Homework 12 (28 November, 2011)
1) 11.59, p672 (CLT) batteries. Continuity correction.
2) 11.2 p639: (MGF Poisson)
3) 11.61, p673 (CLT) incomes
4) 11.91, p679 (CLT) genetics
5) 11.95 p680 (CLT) test scores