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Statistics — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSStatistics1 Mark
Question
If X and Y are two variates connected by the relation $\text{Y}=\frac{\text{aX+b}}{\text{c}}$ and $\text{Var}(\text{X})=\sigma^2,$ then write the expression for the standard deviation of Y.
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Answer

We know that if $y_i=a x_i+b$, then $\operatorname{var}(Y)=a^2[\operatorname{Var}(X)]$
Here, $\text{Y}=\frac{\text{aX+b}}{\text{c}}=\frac{\text{a}}{\text{c}}\text{X}+\frac{\text{b}}{\text{c}}$ Therefore, $\text{Var}(\text{Y})=\frac{\text{a}^2}{\text{c}^2}[\text{var}(\text{X})]=\frac{\text{a}^2\sigma^2}{\text{c}^2}$. $\text{S.D.}=\Big|\frac{\text{a}}{\text{c}}\Big|\sigma$

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