Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing annual percent return for Vanguard Total Stock Index (all stocks). Let y be a random variable...


Do bonds reduce the overall risk of an investment portfolio? Let
x
be a random variable representing annual percent return for Vanguard Total Stock Index (all stocks). Let
y
be a random variable representing annual return for Vanguard Balanced Index (60% stock and 40% bond). For the past several years, we have the following data.

































x:
21


0


12


11


31


21


11


−14


−17


−8


y:
8


−2


26


14


15


21


13


−2


−2


−2




(a) Compute Σx, Σx
2, Σy, Σy
2.















Σx
Σx
2
Σy
Σy
2


(b) Use the results of part (a) to compute the sample mean, variance, and standard deviation for
x
and for
y. (Round your answers to four decimal places.)
























x

y
x

s
2

s


(c) Compute a 75% Chebyshev interval around the mean for
x
values and also for
y
values. (Round your answers to two decimal places.)



















x

y
Lower Limit
Upper Limit



Jun 07, 2022
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