If the arithmetic mean of the numbers `x_1, x_2, x_3, ..., x_n` is `barx,` then the arithmetic mean of the numbers `ax_1 +b, ax_2 +b, ax_3 +b, ....,ax_n +b,` where a, b are two constants, would be

If the arithmetic mean of the numbers x_1 , x_2, x_3,……., x_n is barx , then the arithmetic mean of the numbers ax_1 + b, ax_2 + b, ax_3 + b, ……, ax_n + b , where a and b are two constants, would be:

Given that bar x is the mean and sigma^2 is the variance of n observations x_1 , x_2 ,.... x_n . Prove that the mean and variance of the observations ax_1, ax_2, ax_3 ,......, ax_n are a bar x and a^2 sigma^2 , respectively, (a ne 0) .

If the arithmetic mean of the roots of x^(2)-2ax+b=0 is A and the geometric mean of the roots of x^(2)-2bx+a^(2)=0 is G, then

prove that E(ax+b)=aE(x)+b where a and b are constants

If x is the mean of x_1, x_2, ..... ,x_n , then for a ne0 , the mean of ax_1, ax_2, .... ,ax_n,(x_1)/a,(x_2)/a,....,(x_n)/a is

Given that bar x is the mean and sigma^2 is the variance of n observations x_1, x_2, ... x_n . Prove that the mean and variance of the observations ax_1, ax_2, ... ,ax_n , are a bar x and a^2 sigma^2 respectively (a ne 0) .