Let the observations $x_{i}(1 \leq i \leq 10)$ satisfy the equations,
$\sum_{i=1}^{10}\left(x_{i}-5\right)=10$ and $\sum_{i=1}^{10}\left(x_{i}-5\right)^{2}=40$. If $\mu$ and $\lambda$ are the
mean and the variance of the observations, $x_{1}-3, x_{2}-3, \ldots$
$x_{10}-3$, then the ordered pair $(\mu, \lambda)$ is equal to:
Correct Option: 1
Mean of the observation $\left(x_{i}-5\right)=\frac{\Sigma\left(x_{i}-5\right)}{10}=1$
$\therefore \quad \lambda=\left\{\right.$ Mean $\left.\left(x_{i}-5\right)\right\}+2=3$
Variance of the observation
$\mu=\operatorname{var}\left(x_{i}-5\right)=\frac{\Sigma\left(x_{i}-5\right)^{2}}{10}-\frac{\Sigma\left(x_{i}-5\right)}{10}=3$
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