If the variance of observations {x_1},,{x_2}, | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

Varivence of $x_1 \cdot x_2 \cdot \cdots \quad x_n=6^2$

Variane of $a x_1 a x_2, \ldots a x_n=$ ?

varience $=\sigma^2=\frac{1}{n} \sum \limits_{

Vedclass · Accepted Answer

${a^2}{\sigma ^2}$

Vedclass · Answer

Varivence of $x_1 \cdot x_2 \cdot \cdots \quad x_n=6^2$

Variane of $a x_1 a x_2, \ldots a x_n=$ ?

varience $=\sigma^2=\frac{1}{n} \sum \limits_{i=1}^r y_i\left(n_i-\bar{x}ight)^2$

If each obs is weltiplied $2 y$ a the $y_i=a x_i \quad i . e \quad x_i=\frac{1}{a} y_i$

$y_i=a x_i n$

$	herefore \bar{y}=\frac{1}{n} \sum\limits_{i=1}^n y_i=\frac{1}{n} \sum\limits_{i=1}^n a x_i=\frac{a}{n} \sum\limits_{i=1}^n x_i=a \bar{x} .$

${\left[\because \bar{x}=\frac{1}{n} \sum\limits_{i=1}^n x_iight]}$

$(1) \Rightarrow \quad \sigma^2=\frac{1}{A} \sum_{i=1}^n\left(\frac{1}{a} y_i-\frac{1}{a} \bar{y}ight)^2$

$\Rightarrow a a^2 \sigma^2=\frac{1}{n} \sum_{i=1}^n\left(y_i-\bar{y}ight)^2$

These varieme of new obs' is $a^2 \sigma^2$

If the variance of observations ${x_1},\,{x_2},\,......{x_n}$ is ${\sigma ^2}$, then the variance of $a{x_1},\,a{x_2}.......,\,a{x_n}$, $\alpha \ne 0$ is

Similar Questions

If the variance of $10$ natural numbers $1,1,1, \ldots ., 1, k$ is less than $10 ,$ then the maximum possible value of $k$ is ...... .

In a series of $2n$ observation, half of them are equal to $'a'$ and remaining half observations are equal to $' -a'$. If the standard deviation of this observations is $2$ then $\left| a \right|$ equals

The $S.D$ of $15$ items is $6$ and if each item is decreased or increased by $1$, then standard deviation will be

The $S.D.$ of a variate $x$ is $\sigma$. The $S.D.$ of the variate $\frac{{ax + b}}{c}$ where $a, b, c$ are constant, is