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Chebyshev's theorem

  1. Feb 24, 2010 #1
    1. do bonds reduce the overall risk of an investment portfolio? let x be a random variable representing annual % return for Vangaurd Total Stock Index (all stocks). Let y be a random variable representing annual return for Vangaurd Balanced Index(60% stock and 40% bond). For the past several years we have the following data.

    x: 11 0 36 21 31 23 24 -11 -11 -21
    y: 10 -2 29 14 22 18 14 -2 -3 -10

    a.) Compare Ex, Ex2, Ey and Ey2 (2 = squared)

    b.) use results in part (a) to compute the sample mean, variance, and standard deviation for x and for y.

    c.) Compute a 75 % Chebyshev interval about the mean for x values and also for y values. Use interval to compare funds.

    I was able to do part a & b but have no idea what they want for c. i do have the answer but i am not sure what they used to get the answer.

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Feb 25, 2010 #2


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    What is a Chebyshev interval?
  4. Feb 26, 2010 #3


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    There are two possibilities - I'm not sure what level of work you're at.

    First (and simplest): how many standard deviations around the mean does chebyshev's theorem say you must go to include 75% of the data values? (remember chebychev's theorem says the percentage of values between [tex] \bar x \pm ks [/tex] is at least
    [tex] 1 - {1}/{k^2}[/tex].

    Second (and more complicated) is the idea discussed at the following link:

    I'm guessing it is option 1 you need to use.
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