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.

If x1, x2, x3,....xn are n values of a variable X such that Find the value of n and the mean.

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.

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 x_1, x_2, ,\ x_n are n values of a variable X\ a n d\ y_1, y_2, ......,yn are n values of variable Y such that y_i=a x_i+b , i=1,2,\...., n then write Va r\ (Y) in terms of Va r(X)

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.

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.

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.

Let x_1, x_2, ...... ,x_n be values taken by a variable Xa n dy_1, y_2,.......... ,y_n be the values taken by a variable Y such that y_i=a x_i+b ,i=1,2, ,ndot Then, (a) V a r(Y)=a^2V a r(X) (b) V a r(X)=a^2V a r(Y) (c) V a r(X)=V a r(X)+b (d) none of these

If x_(1), x_(2), ………,x_(n) are n values of a variable x such that sum(x_(i)-3) = 170 and sum(x_(i)-6) = 50. Find the value of n and the mean of n values.

Find the least value of n such that (n-2)x^2+8x+n+4>0,AAx in R ,w h e r en in Ndot