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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 16 0 22 16 32 18 25 -13 -19 -10
V. 21 -6 19 8 21 21 26 -9
-7
-7
(a) Compute Ex, Ex2, Zy, Zy2.
Ex
Ex 2
Ey
(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 two
decimal places.)
(c) Compute a 75% Chebyshev interval around
the mean for x values and also for y values.
(Round your answers to two decimal places.)
Lower Limit
Upper Limit
Use the intervals to compare the two funds.
75%% of the returns for the balanced fund fall within a narrower range than those of the stock fund.
75% of the returns for the stock fund fall within a narrower range than those of the balanced fund.
25% of the returns for the balanced fund fall within a narrower range than those of the stock fund.
25% of the returns for the stock fund fall within a wider range than those of the balanced fund.
(d) Compute the coefficient of variation for each