If each of the observation x1,x2,………..xn is increased by 'a',where a is a negative or positive number,shows that the variance remains unchanged.

Differentiate a^x w.r.t. x , where a is a positive constant.

Prove that the function f(x)=x^n is continuous at x=n, where n is a positive integer.

Given that barx Is the mean and sigma^2 is the variance of n observations x_1,x_2, x_3,………….x_n prove that the mean and variance of the observations ax_1,ax_2,ax_3,………ax_n are abarx and a^2sigma^2 respectively. (ane0)

The mean and variance of n observations x_(1), x_(2), x_(3),……..,x_(n) are 5 and 0 respectively. If sum_(i=1)^(n) x_(i)^(2) = 400 , then the value of n is equal to

The variance of 20 observations is '5 .' If each observation is multiplied by 2, find the new variance of the resulting observations.

The mean of 5 observations is 4.4 and their variance is 8.24.If three of the observations are 1,2 and 6,find the other two observations.

Let a pair of dice be thrown and the random variable X be the sum of the numbers that appear on the two dice. Find variance of X.