Question

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

Answer 1

Hint: 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.