HW 2B
Overall your best 10 of 13 Part B submissions will account for 15% of your overall course grade
(with each one of your best 10 accounting for 1.5% of your overall course grade).
But to make the
grading easier, I'll make this assignment worth 150, and I'll
assign only integer scores for each part. So each point indicated below
is really only worth 0.01% of your overall course grade.
There are 4 parts to this assignment worth
50 points each, but I'll only count your best 3 of 4 parts. So each of your best 3 parts will account for 0.5% of your overall course grade. (I do realize that
this may tempt some to not do the homework, but the way I look at it is that overall, for the whole semester,
homework will account for 25% of the overall course grade ... and that seems about right to me, since I
like to put emphasis on good exam performance (and especially final exam performance since it measures what
one knows at the end of the course). I think taking the homework seriously will be a great help in learning the material
covered and preparing yourself for the exams.)
1) (50 points)
Do part (b) of Problem 21 on p. 52 of Ross for the case of i = 3 (and only for the case of i = 3).
Consider all of the children from all of the families, and suppose that each child is just as likely to be selected as any of the other children.)
Provide a brief written explanation to indicate
how you arrived at your final answer. (Be careful; the answer is not 5/20 = 1/4. (5/20 = 1/4 is the answer for part (a)
of this problem for the case of i = 3.))
2) (50 points)
Do part (a) of Problem 28 on p. 52 of Ross. Assume the balls are drawn without replacement (i.e., a subset of three different balls from the
19 will be drawn). Don't do the sampling with replacement variation that is described after part (b) of the problem.
Show adequate work
to justify your answer (which should be given as a number (and not left in terms of factorials, binomial coefficients, etc.)).
3) (50 points)
Do part (a) of Problem 35 on p. 53 of Ross. Assume the balls are drawn without replacement (i.e., a subset of seven different balls from the
46 will be drawn). (Don't consider sampling with replacement.)
While you don't have to provide a detailed justification for your
answer (which should be given as a number (and not left in terms of factorials, binomial coefficients, etc.)), you should provide
an expression which indicates where your final answer comes from.
4) (50 points)
Do part (a) of Problem 43 on p. 53 of Ross.
Provide adequate justification for your answer (which should be given as a function of N which is simplified as much as possible).
Make the usual assumptions (i.e., suppose that all possible arrangements of the people in a line are equally likely).