UPSC Statistics PYQs 2024 | Vaidra

1Mediummains20 marks

Statistics

(a) Obtain the control limits for X̄-chart and R-chart and describe the significance of joint study of these charts.

(b) Find the reliability and hazard functions of Weibull distribution with scale parameter θ and shape parameter β, and interpret the findings.

Maximise z = 5x₁ + 2x₂

subject to 6x₁ + x₂ ≥ 6,

4x₁ + 3x₂ ≥ 12,

x₁ + 2x₂ ≥ 4,

x₁ ≥ 0, x₂ ≥ 0.

2Medium10 marks

For the population U = {a, b, c, d, e}, consider the following sampling design : P({a, b, d}) = 1/6, P({a, b, e}) = 1/6, P({a, d, e}) = 1/6, P({b, c, d}) = 1/6, P({b, c, e}) = 1/6, P({c, d, e}) = 1/6 Calculate the first-order and second-order inclusion probabilities. Hence show that it is a matter of a stratified design. Identify the strata with their units.

3Medium10 marks

(i) Determine the average age at death of those who die between ages x and x + n.

(ii) If l(x) = 100 \sqrt{100 - x} find mu(84) exactly using appropriate method.

Statistics UPSC PYQ 2024

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