Stat 225 – Problem Set 09
Hints
Spring 2009
1.
(a) The quantity of interest is a
count
.
(b) Use the distribution from (a). Ans. 14.
(c) Use the distribution from (a). Ans. 0.183.
(d) The number of requests in nonoverlapping time intervals are independent.
(e) The quantity of interest is a
waiting time
.
(f) Use the distribution in (e). Ans. 0.143.
(g) Use the distribution in (e). Ans. 0.03.
2.
(a) The quantity of interest is a
count
.
(b) Use the distribution in (a) and the independence of nonoverlapping time in
tervals. Ans. 0.00085
(c) Need a different distribution from that in (a). Ans. 0.0378.
(d) 12 customers per hour in each of the first three hours is only one of many ways
that 36 customers could arrive in the first three hours.
3.
(a)
W
is a
waiting time
.
(b) Ans. 0.1 hours.
(c) It takes longer than
1
6
hours for the first customer to arrive.
(d) Note that the number of customers between 9:00 and 9:15 is
known
.
(e) Use definition of conditional probability and the Uniform CDF.
(f) Say that a customer arriving between 9:30 and 10:00 is a “success.” Then
Z
is the number of “successes” out of ten.
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 Spring '08
 MARTIN
 Conditional Probability, Probability, Cumulative distribution function, nonoverlapping time intervals

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