Question

What is the standard deviation of $\sigma (X) = \dfrac{{\sigma (Y)}}{2}$, what is $\sigma (X - Y)$?

Answer 1

Standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range.

Complete step by step solution:
The Standard Deviation is a measure of how spread-out numbers are. Its symbol is $\sigma$ (the Greek letter sigma). The formula is easy: it is the square root of the Variance i.e.
$\sqrt {\sum\limits_{i = 1}^n {{{({X_i} - \bar X)}^2}} }$
Here $\bar X$ is the expected value of the data set and $X$ is the actual value of the dataset.
In the given case we are provided with a continuous function. A continuous function is a real-valued function whose graph does not have any breaks or holes. It is fully defined at a single point.
$\sigma (X - Y)$ is the sum of the differences between an expected response $X$ from a model and the actual data $Y$from the range of data collected. It is used in the calculation of variance and standard deviations.
The standard deviation of a defined continuous function is zero because by its definition each $X$ data point corresponds exactly to each $Y$ data point. Due to such correspondence, there will be no deviation to calculate.

Hence, we can conclude that the standard deviation of the given question is $\sigma (X - Y) = 0$.

Note:

Here it is assumed that $Y$ is referring to the actual data.
Standard deviation may be abbreviated SD
Standard deviation should be carefully analysed before reaching a conclusion. Variance cannot be negative but standard deviation can be negative.