Transformation of Mean and Variance

Rarely Tested

Transformation of Mean and Variance

For:

$$y=a+bx$$

the mean is:

$$\bar{y}=a+b\bar{x}$$

and variance is:

$$\sigma_y^2=b^2\sigma_x^2$$

Usage

- Gives the complete transformation of mean and variance under a linear change.

Question 1

The mean and variance of a dataset are $$10$$ and $$4$$ respectively. If all values are transformed by $$y = 2x + 3,$$ find the new variance

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