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.

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

If the mean of n observations x_1,x_2,x_3...x_n is barx then the sum of deviations of observations from mean is

Let x_(1),x_(2),……,x_(n) be n observations and barx be their arithmetic mean. The formula for the standard deviation is

Given that bar x is the mean and sigma^2 is the variance of n observations x_1x_2 , ..., x_n . Prove that the mean and variance of the observations a x_1,a x_2 , a x_3,dotdotdot,a x_n are a bar x and a^2sigma^2 ,

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 x_(1), x_(2), x_(3), x_(4),x_(5) be the observations with mean m and standard deviation s. The standard deviation of the observations kx_(1), kx_(2), kx_(3), kx_(4), kx_(5) is

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 be values taken by a variable X a n d y_1, y_2,.......... ,y_n be the values taken by a variable Y such that y_i=a x_i+b ,i=1,2,3.... Then, (a) Var.(Y)= a^2Var.(X) (b) Var.(X)=a^2Var.(Y) (c) Var.(X)=Var.(X)+b (d) none of these

If the standard deviation of x_(1),x_(2),….,x_(n) is 3.5 then the standard deviation of -2x_(1)-3, -2x_(2)-3,….,-2x_(n)-3 is

Let X denote the sum of the numbers obtained when two fair dice are rolled. Find the variance and standard deviation of X.