Statistics UPSC PYQ 2023

State and discuss the important points which have to be considered in the construction of index numbers. <!--qid:MAINS_2023_Statistics-II_Q5-->

Suppose that the life in hours of an electric gadget manufactured by a certain process is normally distributed with parameters μ = 160 hours and some σ. What would be the maximum allowable value of σ if the life X of the gadget is to have a probability 0.80 of being between 120 hours and 200 hours? (Normal distribution Table is given at the end.) <!--qid:MAINS_2023_Statistics-II_Q4-->

Derive, by starting from a suitable functional form for lx, the formula (i) Lx = (lx + lx+1)/2 and (ii) Lx = (lx − lx+1)/(log lx − log lx+1) = − dx / log px (iii) e0x = 1/2 + Σ_{i=1}^{∞} i dx+i / lx where lx = members of the cohort alive at age x Lx = number of years lived, in the aggregate, by the cohort of l0 persons between age x and (x + 1) dx = number of persons dying between age x and (x + 1) = lx − lx+1 px = probability that a person of age x will survive till age (x + 1) e0x = expectation of life at age x <!--qid:MAINS_2023_Statistics-II_Q7-->

Explain the principle of least squares. How is it used in fitting trend in time-series analysis? Explain the fitting of trend for the curve y = a bᵗ c^{t²}. <!--qid:MAINS_2023_Statistics-II_Q6-->

Explain the method of collection of agriculture data. Describe the (i) official publications for data collection, and (ii) statistics collected by the various official agencies pertaining to agriculture production. Official publications for data collection. Statistics collected by the various official agencies pertaining to agriculture production. <!--qid:MAINS_2023_Statistics-II_Q8-->