If each observation of a distribution with va | vedclass

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

Question

(C) We know that for a random variable $X$,the variance of $aX$ is given by $\operatorname{Var}(aX) = a^2 \cdot \operatorname{Var}(X)$.Given that the

Vedclass · Accepted Answer

$|\lambda| \sigma$

Vedclass · Answer

(C) We know that for a random variable $X$,the variance of $aX$ is given by $\operatorname{Var}(aX) = a^2 \cdot \operatorname{Var}(X)$.Given that the original variance is $\sigma^2$,the variance of the new observations (where each observation is multiplied by $\lambda$) is $\operatorname{Var}(\lambda X) = \lambda^2 \cdot \operatorname{Var}(X) = \lambda^2 \sigma^2$.The standard deviation is the square root of the variance.Therefore,the new standard deviation is $\sqrt{\lambda^2 \sigma^2} = |\lambda| \sigma$.

If each observation of a distribution with variance $\sigma^2$ is multiplied by $\lambda$,find the standard deviation of the new observations.

Similar Questions

Let $n$ observations $x_1, x_2, ....., x_n$ be such that $\sum {x_i}^2 = 400$ and $\sum x_i = 80$. Then,which of the following is a possible value for $n$?

The variance of $20$ observations is $5$. If each of the observations is multiplied by $2$,then the variance of the resulting observations is:

The variance of the first $10$ natural numbers which are multiples of $3$ is

Find the standard deviation of the first $n$ natural numbers.

If the mean of the discrete distribution $8, 9, 6, 5, x, 4, 6, 5$ is $6$,then its standard deviation (nearest to two decimal places) is

Vedclass Test Series

Exam Paper Generator

Online Exam Module