If each of the observations `x_(1),x_(2)….x_(n)` is in - creased by k. where k positive or negative number, then show that the variance remains unchanged.

If each of the observation x_1,x_2,dotdotdot,x_n is increased by a where a is a negative or positive number, show that the variance remains unchanged.

Let x_1, x_2, x_3, , be n values of a variable X. If these values are changed to x_1+a ,x_2+a , ....., x_n+a ,w h e r ea in R , show that the variance remains unchanged.

Let f(x)=((x-3)(x+2)(x+6))/((x+1)(x-5)) Find intervals where f(x) is positive or negative

If the standard deviation of n observation x_(1), x_(2),…….,x_(n) is 5 and for another set of n observation y_(1), y_(2),………., y_(n) is 4, then the standard deviation of n observation x_(1)-y_(1), x_(2)-y_(2),………….,x_(n)-y_(n) is

The number non-negative integral solutions of x_(1)+x_(2)+x_(3)+x_(4) le n (where n is a positive integer) is:

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

If X is a random variable with the following distribution where p+q=1 then show that the variance of X is pq(a-b)^(2) .

The expression 1/3x^2-2 can be rewritten as 1/3(x-k)(x+k) , where k is a positive constant . What is the value of k ?

The number of non-negative integral solution x_1 + x_2 + x_3 + x_4 <=n (where n is a positive integer) is :

Let x_1,\ x_2,\....,\ x_n values of variable X and let 'a' be non zero real number. Then prove that the variance of the observations a x_1,\ a x_2, ... ,\ a x_n is a^2 Var (X) . Also, find their standard deviation.