Do bonds reduce the overall risk of an investment portfolio? Letx be a random variable representing annual percent return forVanguard Total Stock Index (all stocks). Let y be a random variablerepresenting annual return for Vanguard Balanced Index (60% stockand 40% bond). For the past several years, we have the followingdata. x: 30 0 20 12 19 18 23 ?22 ?24 ?21 y: 11 ?5 9 8 21 25 22 ?3?7 ?2 (a) Compute ?x, ?x2, ?y, ?y2. ?x ?x2 ?y ?y2 (b) Use theresults of part (a) to compute the sample mean, variance, andstandard deviation for x and for y. (Round your answers to twodecimal places.) x y x s2 s (c) Compute a 75% Chebyshev intervalaround the mean for x values and also for y values. (Round youranswers to two decimal places.) x y Lower Limit Upper Limit Use theintervals to compare the two funds. 75% of the returns for thebalanced fund fall within a narrower range than those of the stockfund. 75% of the returns for the stock fund fall within a narrowerrange than those of the balanced fund. 25% of the returns for thebalanced fund fall within a narrower range than those of the stockfund. 25% of the returns for the stock fund fall within a widerrange than those of the balanced fund. (d) Compute the coefficientof variation for each fund. (Round your answers to the nearestwhole number.) x y CV % % Use the coefficients of variation tocompare the two funds. For each unit of return, the stock fund haslower risk. For each unit of return, the balanced fund has lowerrisk. For each unit of return, the funds have equal risk. If srepresents risks and x represents expected return, then s/x can bethought of as a measure of risk per unit of expected return. Inthis case, why is a smaller CV better? Explain. A smaller CV isbetter because it indicates a higher risk per unit of expectedreturn. A smaller CV is better because it indicates a lower riskper unit of expected return.