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.

Solve (x - 1)^n =x^n , where n is a positive integer.

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) .

Assertion (A) : The number of positive integral solutions of x_(1)+x_(2)+x_(3)=10 is 36. Reason (R) : The number positive integral solutions of the equation x_(1)+x_(2)+x_(3)+.......+x_(k)=n is ""^(n-1)C_(k-1) , The correct answer is

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

If one of the zeros of the quadratic polynomial f(x) = 14x^(2) -42k^(2)x-9 is negative of the other then k = ………………

The standard deviation of n observations x_(1), x_(2), x_(3),…x_(n) is 2. If sum_(i=1)^(n) x_(i)^(2) = 100 and sum_(i=1)^(n) x_(i)^(2) = 20 show the values of n are 5 or 20

Find the left hand derivative of f (x) =[x] sin pi, x , at x=k where k is an integer.