Given thatisthe mean and σ2is the variance of n observations x1, x2… xn Prove that the mean andvariance of - Maths - Statistics

Question

Given thatisthe
mean and σ2is the variance of n observations
x 1, x 2… x
n Prove that the mean andvariance of the
observations ax 1, ax
2,ax 3 …ax
n are and
a 2 σ2,respectively (a
≠ 0)

Global Expert · Accepted Answer

The givenn observations are x1, x2… xn Mean =

Variance =σ2

If eachobservation is multiplied by a and the new observations areyi, then

Therefore,mean of the observations, ax1, ax2… axn, is

Substitutingthe values of xiand

in(1), we obtain

Thus, thevariance of the observations, ax1, ax2… axn, is a2 σ2

Given thatisthe mean and σ2is the variance of n observations x 1, x 2… x n . Prove that the mean andvariance of the observations ax 1, ax 2,ax 3 …ax n are and a 2 σ2,respectively (a ≠ 0).

Given thatisthe mean and σ²is the variance of n observations x ₁, x ₂… x _n. Prove that the mean andvariance of the observations ax ₁, ax ₂,ax ₃ …ax _nare and a ² σ²,respectively (a ≠ 0).