The coefficient of variation for a sample ofvalues x 1 ,x 2 , · ·· , xn is defin
ID: 2914925 • Letter: T
Question
The coefficient of variation for a sample ofvalues x1,x2, · ·· , xn is definedby C.V. = s/¯x , wheres is the sample
standard deviation and ¯xis thesample mean. This term gives the standard deviation as a proportionof the
mean, and it is sometimes an informative quantity. Forexample a value of s = 10 has littlemeaning unless
we can compare it with something else. Ifs = 10 and ¯x= 1000the amount of variation is small relative
to the mean. However, if s= 10and ¯x = 5 then the variationis quite large relative to the mean. If we
were studying the precision (variation in repeatedmeasurements) of a measuring instrument, the firstcase
C.V. = 10/1000might givequite acceptable precision but the second caseC.V. = 10/5 would be quiteunacceptable.
Let x1, x2,·· · , x10denote arandom sample of size 10 from a normal distribution with mean 0 andvariance
^2.
a. Find the distribution of (10¯x^2)/s2 .
b. Find the distribution of s2/(10¯x2).
c. Find the number csuchthat P(c < s/¯x <c) = 0.95.