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Paper 1 – Unbiased Estimates
Example
The number of breakdowns on a road in a city is studied . A sample of 20 observations is recorded on 20 different days . Let X be the number of breakdowns on a particular day . It is given that s � 3.8 .
2 n
( a ) Find
s �
.
2 n 1
Let X be the mean of the sample . It is also given that there are 60 breakdowns in these 20 days .
[ 2 ]
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( b ) Find an unbiased estimate of the population mean . [ 2 ]
Solution
( a )
n s � � s n �1
2 2 n 1 n
2 sn � 1
20 � ( 3 . 8 )
20 �1
s �
� A1
2 n 1
4
( b ) An unbiased estimate
( A1 ) for substitution
� X ( A1 ) for correct approach
60 �
20 � 3
A1
[ 2 ]
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