Let $x_{1}, x_{2}, \ldots, x_{n}$ be $n$ observations, and let $\bar{x}$ be their arithmetic mean an

Question

Let $x_{1}, x_{2}, \ldots, x_{n}$ be $n$ observations, and let $\bar{x}$ be their arithmetic mean and $\sigma^{2}$ be their variance. Statement 1: Variance of $2 x_{1}, 2 x_{2}, \ldots ., 2 x_{n}$ is $4 \sigma^{2}$. Statement 2: Arithmetic mean of $2 x_{1}, 2 x_{2}, \ldots ., 2 x_{n}$ is $4 \bar{x}$.

Professor PC Thomas Classes · Answer

(b) : Given, $x_{1}, x_{2}, x_{3}, \ldots ., x_{n}$, be $n$ observations.\ A.M. $=\bar{x}$ and Variance $=\sigma^{2}$ Statement 2 : A.M. of $2 x_{1}, 2 x_{2}, \ldots ., 2 x_{n}$\ $=\frac{2\left(x_{1}+x_{2}+\ldots . .+x_{n}ight)}{n}=2 \bar{x}$\ Given A.M. $=4 \bar{x}$\ $	herefore \quad$ Statement 2 is false.\