The coefficient of variation

(CV)

for a random sample

Y_(1),dots,Y_(n)

is defined by\

CV=(S)/((/bar (Y)))

\ where

S

is the sample standard deviation and

/bar (Y)

is the sample mean.

CV

measures the amount of\ variation as a proportion of the sample mean. Suppose each

Y_(i)N(0,\\\\sigma ^(2))

for

i=1,dots,10

.\ (a) By using

F_(1,v)-=t_(v)^(2)

, find the distribution of

(10)/(b)ar ((Y)^(2))/(S^(2))

in terms of the

F

-distribution.\ (b) Find the distribution of

(S^(2))/((10)/(b)ar (Y)^(2))

.\ (c) Using statistical tables, find the number

c

such that\

Pr{-c

The coefficient of variation (CV) for a random sample Y1,,Yn is defined by CV=YS where S is the sample standard deviation and Y is the sample mean. CV measures the amount of variation as a proportion of the sample mean. Suppose each YiN(0,2) for i=1,,10. (a) By using F1,vtv2, find the distribution of 10Y2/S2 in terms of the F-distribution. (b) Find the distribution of S2/(10Y2). (c) Using statistical tables, find the number c such that Pr{cYSc}=.95