In a series of 20 observations, 10 observations are each equal t k, and each of the remaining halves is equal to –k. If the standard deviation of the observation is 2, then write the value of k.

If x₁, x₂, ……, x_n are n values of a variable X and y₁, y₂, ……., y_n are n values of variable Y such that y_i = ax_i + b, i = 1,2, ……, n, then write Var(Y) in terms of Var(X).

If X and Y are two variates connected by the relation and , then write the expression for the standard deviation of Y.

If each observation of a raw data whose standard deviation is σ is multiplied by a, then write the S.D. of the new set of observations.

If a variable X takes values 0, 1, 2, ….., n with frequencies ⁿC₀, ⁿC₁, ⁿC₂, …….ⁿC_n, then write variance X.