Let set X contain 10 observations with a mean of 3 and a variance of 5 . Let set Y contain 20 observations with a mean of 34 and a variance of 8 . A new set Z is formed by replacing each observation x in set X with 2x + 4 , and replacing each observation y in set Y with y 2 - 1 . The variance of the combined set Z is

Step-by-step solution

Let the transformed sets be X' and Y' . For set X' , the transformation is x' = 2x + 4 . The new mean is _ X' = 2(3) + 4 = 10 . The new variance is V_ X' = 2^2 5 = 20 . For set Y' , the transformation is y' = y 2 - 1 . The new mean is _ Y' = 34 2 - 1 = 16 . The new variance is V_ Y' = ( 1 2 )^2 8 = 1 4 8 = 2 . Now, combine sets X' and Y' to form set Z . The total number of observations is 10 + 20 = 30 . The combined mean of set Z is: _Z = 10 10 + 20 16 30 = 100 + 320 30 = 14 The differences between the individual m