Let X = {x ∈ N: 1 ≤ x ≤ 17} and Y = {ax + b: x ∈ X and a, b ∈ R, a 0}. If mean and variance of elements of Y are 17 and 216 respectively then a + b is equal to:

Question

Let X = {x ∈ N: 1 ≤ x ≤ 17} and Y = {ax + b: x ∈ X and a, b ∈ R, a > 0}. If mean and variance of elements of Y are 17 and 216 respectively then a + b is equal to:

Accepted Answer

−7. For x in 1..17, mean = 9 and variance = 24. With Y = ax+b: variance of Y = a^2*24 = 216 -> a = 3 (a>0); mean of Y = 9a+b = 17 -> b = 17-27 = -10. So a+b = 3-10 = -7.

Let X = {x ∈ N: 1 ≤ x ≤ 17} and Y = {ax + b: x ∈ X and a, b ∈ R, a > 0}. If mean and variance of elements of Y are 17 and 216 respectively then a + b is equal to:

Solution

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