If two variates `Xa n dY` are connected by the relation `Y=(a X+b)/c ,w h e r ea ,b ,c` are constants such that `a c<0,t h e n`
(a) `sigma_gamma=a/csigma_X` (b) `sigma_gamma=-a/csigma_X`
(c) `sigma_gamma=a/csigma_X+b`
(d) none of these

Explanation

If two variates `X andY`
are connected by the relation `Y=(a X+b)/c` then

`Y=\frac{aX+b}{c}`

`Y=\frac{\sum_{i=1}^{n}\frac{aX+b}{c}}{n}`

`Y=\frac{\frac{a\sum_{i=1}^{n}X+nb}{c}}{n}`

`Y=\frac{\frac{a}{c}\sum_{i=1}^{n}X}{n}+\frac{b}{c}`

`V(X)=\frac{\sum_{i=1}^{n}(x_{i}-X)^2}{n}=\sigma ^2`

`V(Y)=\frac{\sum_{i=1}^{n}(y_{i}-Y)^2}{n}`

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