Dear Student, Let σx = σLet y = ax+bcNow, y = ax+bc = acx + bcNow, Vary = σy2 = 1n∑i=1nyi - y2=1n∑i=1naxi+bc -acx + bc 2=1n∑i=1naxi + axc2=a2c2×1n∑i=1nxi - x2=a2c2 × Varx=a2c2×σx2⇒σy2 =a2c2×σx2⇒σy = ac×σx⇒σy = |ac|σ as, σx = σ So, option (b) is correct Regards

Please solve this....

Dear Student,

Let σ_{x} = σ Let y = \frac{ax + b}{c} Now, y = (\frac{ax + b}{c}) = \frac{a}{c} x + \frac{b}{c} Now, Var (y) = {σ_{y}}^{2} = \frac{1}{n} \sum_{i = 1}^{n} {(y_{i} - y)}^{2} = \frac{1}{n} \sum_{i = 1}^{n} {[\frac{{ax}_{i} + b}{c} - (\frac{a}{c} x + \frac{b}{c})]}^{2} = \frac{1}{n} \sum_{i = 1}^{n} {[\frac{{ax}_{i} + a x}{c}]}^{2} = \frac{a^{2}}{c^{2}} \times \frac{1}{n} \sum_{i = 1}^{n} {(x_{i} - x)}^{2} = \frac{a^{2}}{c^{2}} \times Var (x) = \frac{a^{2}}{c^{2}} \times {σ_{x}}^{2} \Rightarrow {σ_{y}}^{2} = \frac{a^{2}}{c^{2}} \times {σ_{x}}^{2} \Rightarrow σ_{y} = |\frac{a}{c}| \times σ_{x} \Rightarrow σ_{y} = | \frac{a}{c} | σ [as, σ_{x} = σ]

So, option (b) is correct.

Regards

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