A) \[\log {{G}_{1}}+\log {{G}_{2}}+....+\log {{G}_{n}}\]
B) \[{{G}_{1}}{{G}_{2}}....{{G}_{n}}\]
C) \[\log {{G}_{1}},\log {{G}_{2}},....,\log {{G}_{n}}\]
D) None of the above
Correct Answer: B
Solution :
Taking\[x\]as the product of variates\[{{x}_{1}},{{x}_{2}},.....,{{x}_{r}}\]corresponding to r set of observation ie, \[x={{x}_{1}}{{x}_{2}}.....{{x}_{r}},\]we have \[\log x=\log \text{ }{{x}_{1}}+\log \text{ }{{x}_{2}}+...+\log \text{ }{{x}_{r}}\] \[\Rightarrow \] \[\Sigma \log x=\Sigma \log \text{ }{{x}_{1}}+\Sigma \log \text{ }{{x}_{2}}+...+\Sigma \log \text{ }{{x}_{r}}\] \[\Rightarrow \] \[\frac{1}{n}\Sigma \log x=\frac{1}{n}\Sigma \log \text{ }{{x}_{1}}+\frac{1}{n}\Sigma \log \text{ }{{x}_{2}}\] \[+...+\frac{1}{n}\Sigma \log \text{ }{{x}_{r}}\] \[\Rightarrow \] \[\log G=\log {{G}_{1}}+\log {{G}_{2}}+....+\log {{G}_{r}}\] \[\Rightarrow \] \[G={{G}_{1}}{{G}_{2}}......{{G}_{r}}\]
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