THE UNIVERSITY OF HONG KONG
DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE
STAT 1302 PROBABILITY AND STATISTICS II
(200910)
EXAMPLE CLASS 3
1. A coin has a probability
p
to turn up a head when tossed. It was tossed 100
times and 55 heads turned up. Write down the likelihood function.
2. Assume the height of a student is normally distributed with mean
μ
and
variance
σ
2
, the heights of 5 randomly selected students were measured to be
1.76, 1.68, 1.82, 1.75 and 1.78. Write down the likelihood function.
3. A sample of size 10 is drawn at random without replacement from a population
of size
N
= 1000, in which there are
m
males and
N

m
females and
m
is
not known. It is found that there are two males in the selected sample. Write
down the likelihood function.
4. An archer shoots arrows repeatedly at a target until he gets exactly 3 hits. It
may be assumed that the probability for an arrow to hit the target is
p
, and
the shots are independent of one another.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '10
 SMSLee
 Statistics, Probability, Probability distribution, probability density function, Likelihood function, UNIVERSITY OF HONG KONG DEPARTMENT

Click to edit the document details