First slide

Introduction to statistics

Question

$If S.D. of X is σ, then S.D. of the variable U = \frac{a X + b}{c}, where a, b, c are constants, is$

Moderate

A

$|\frac{c}{a}| σ$
B

$|\frac{a}{c}| σ$
C

$|\frac{b}{c}| σ$
D

$\frac{c^{2}}{a^{2}} σ$

Solution

$\begin{array}{l} Var (X) = σ^{2} \\ Var (\frac{a}{c} x) = \frac{a^{2}}{c^{2}} σ^{2} \\ Var (\frac{a}{c} x + \frac{b}{c}) = \frac{a^{2}}{c^{2}} σ^{2} + 0 \\ Var (\frac{aX + b}{c}) = \frac{a^{2}}{c^{2}} σ^{2} \end{array}$
$S.D. of (\frac{aX+b}{c}) = |\frac{a}{c}| σ$

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