Extra Problems From Ch. 4 and Ch. 5
1)
Do part (a) of Problem 4.67 on p. 180 of Ross. Show some work,
and give a numerical value (rounded to 3 significant digits) for the desired probability.
2)
Do Problem 4.78 on p. 181 of Ross.
For this one it's okay to just give a final answer ... you don't need to show all of your work.
(Although you could start with the negative binomial distribution pmf and try to figure out how to modify it
appropriately, I suggest that you start from scratch and derive the desired pmf in a manner similar to what I
used to derive the negative binomial pmf near the middle of p. 4-19 of the class notes.)
3)
Do part (a) of Problem 4.82 on p. 182 of Ross. Show some work,
and give a numerical value (exact, or else rounded to 3 significant digits) for the desired probability.
Assume that the sample is drawn without replacement (i.e., a subset of 10 of the 100 items is randomly selected).
4)
Do part (b) of Problem 4.87 on p. 182 of Ross, except take each of the pi to be 1/5. Show some work,
and give a numerical value (exact, or else rounded to 3 significant digits) for the desired probability.
(Hint: Express the number of boxes having exactly one ball as a sum of five indicator (0/1) random variables.
E.g., let Y =
I1 +
I2 +
I3 +
I4 +
I5 and use a key result from Sec. 4.9 of the text.)
5)
Do Problem 5.1 on p. 228of Ross. Show some work to justify your answer.
6)
Do part (a) of Problem 5.4 on p. 228 of Ross, except give the probability that
X exceeds 25 instead of the probability that
X exceeds 20. Show some work to justify your answer.
7)
Do part (b) of Problem 4.67 on pp. 180 of Ross. Show some work,
and give a numerical value (rounded to 3 significant digits) for the desired probability.
8)
Do part (b) of Problem 4.82 on p. 182 of Ross. Show some work,
and give a numerical value (exact, or else rounded to 3 significant digits) for the desired probability.
Assume that the sample is drawn without replacement (i.e., a subset of 10 of the 100 items is randomly selected).
9)
Do part (a) of Problem 4.87 on p. 182 of Ross, except take each of the pi to be 1/5. Show some work,
and give a numerical value (exact, or else rounded to 3 significant digits) for the desired probability.
(Hint: Express the number of boxes having no balls as a sum of five indicator (0/1) random variables.
E.g., let Y =
I1 +
I2 +
I3 +
I4 +
I5 and use a key result from Sec. 4.9 of the text.)
10)
Do part (b) of Problem 5.4 on p. 228 of Ross.
Provide some justification for your answer (and be sure to express your answer properly ... as a function defined
for all real numbers).