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- Find the range for the following sample data. x 23 17 11 30 27arrow_forwardDo bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing annual percent return for the Vanguard Total Stock Index (all Stocks). Let y be a random variable representing annual return for the Vanguard Balanced Index (60% stock and 40% bond). For the past several years, assume the following data. Compute the sample mean for x and for y. Round your answer to the nearest tenth. x: 11 0 36 22 34 24 25 -11 -11 -22 y: 9 -3 28 14 23 16 14 -3 -4 -9arrow_forwardDo bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing annual percent return for the Vanguard Total Stock Index (all Stocks). Let y be a random variable representing annual return for the Vanguard Balanced Index (60% stock and 40% bond). For the past several years, assume the following data. Compute the range for variable y. X 12 0 36 21 35 23 24 -12 -12 -21 Y 10 -2 26 15 22 18 15 -2 -3 -10arrow_forward
- Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing annual percent return for the Vanguard Total Stock Index (all Stocks). Let y be a random variable representing annual return for the Vanguard Balanced Index (60% stock and 40% bond). For the past several years, assume the following data. Compute the range for variable y. X 12 0 36 21 35 23 24 -12 -12 -21 Y 10 -2 26 15 22 18 15 -2 -3 -10arrow_forwardDo bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing annual percent return for the Vanguard Total Stock Index (all Stocks). Let y be a random variable representing annual return for the Vanguard Balanced Index (60% stock and 40% bond). For the past several years, assume the following data. Compute the range for variable x. X 15 0 37 23 33 25 26 -15 -15 -23 Y 6 -1 28 18 24 17 18 -1 -2 -6arrow_forward7.16. If the probability density of X is given by g kx³ for x>0 f(x) = (1+2x)6 0 10-01, elsewhere trolls inf ( 2X density of the random variable Y = where k is an appropriate constant, find the probability 1+2X distribution of Y, and thus determine the value of k. 7 Identify thearrow_forward
- #2arrow_forward2. We want to find the inverse of f(x) = (x+3)² a. On the graph at right, sketch f(x). (Hint: use what you know about transformations!) (2 points) b. What domain should we choose to get only the part of f (x) that is one- to-one and non-decreasing? Give your answer in inequality notation. (2 points) - c. Now use algebra to find f¯¹ (x). (2 points) -4- 3- 2 1 -4 -3 -2 -1 0 1 -1- -2- --3- -4 -N- 2 3 4arrow_forward1. Suppose f(x) = 2 4 == x+3 and g(x) = ½-½. Find and fully simplify ƒ(g(x)). Be sure to show all x your work, write neatly so your work is easy to follow, and connect your expressions with equals signs. (4 points)arrow_forward
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