Statistics 101 Problem Set #7 Fall 1999
This homework is to be done individually. It is due on the last day
of class.

 Exercise 7.4 page 268
 Exercise 7.5 page 268
 Taxicabs are numbered from 1,2,...,N. We want to estimate N, the
total number of taxicabs. We will observe n (n less than N)
cabs. Denote their number by Y_{1},...,Y_{n}.
We consider two estimators for N:
 Estimator 1 is (2 Ybar  1) where Ybar is the
average of all the Y's observed.
 Estimator 2 is Maximum of
Y_{1},...,Y_{n}.
Assume that the n taxicabs that we will see is a simple random
sample of the N cabs. (Sampling without replacement). We want
to compare estimator 1 to estimator 2. To this end, assume that
N = 4 and n = 2.
 Write down the 4 choose 2 possible samples of taxi
numbers.
 Write down the sampling distribution of teach of the
estimators. (Sketch the probability distribution function.)
 Which of the estimators is unbiased? Note that the true
answer is N = 4.
 Which estimator is closer to 4 on the average, where
closeness is measured by
(estimate  4)^{2}?

 Exercise 7.15 page 273
 Exercise 7.16 page 273
 Exercise 7.17 page 274

 Exercise 7.20 page 276
 Exercise 7.21 page 276

 Exercise 7.25 page 279
 Exercise 7.26 page 279
 Exercise 7.27 page 279

 Exercise 7.72 page 304
 Exercise 7.74 page 304
Last modified: Mon Nov 22 09:51:20 EST 1999