Q1.
() (a) For the sequence of r.v.'s {Xn} with P{Xk = k^λ} = P{Xk = -k^λ} = 1/2, λ > 0. Hence show that if the WLLN holds, central limit theorem holds. r.v.'s {Xn} के अनुक्रम के साथ P{Xk = k^λ}=P{Xk = -k^λ}=1/2, λ > 0.
() (c) The following data represent the yields of maize in q/ha recorded from an experiment : 16.4, 19.2, 24.5, 15.4, 17.3, 23.6, 22.7, 20.9, 18.2. Test whether the median (M) is 20 q/ha. जाँच कीजिए कि माध्यिका (M) 20 q/ha है.
() (d) If the values of the units in the population consists of a linear trend such that Yi = a + bi (i = 1,2,...,N), then prove that Var(\barYst)
