ISS (Statistical Services) Statistics Paper II (Old Subjective Pattern): Questions 20 - 25 of 39

Describe in Detail

Let X be exponentially distributed with parameter θ. Obtain MLE of θ based on a sample of size n, from the above distribution.

Describe in Detail

Let y ₁, y _{2, …,} y _n be a random sample from N (µ, σ ²) where µ and σ ² are both unknown. Obtain a confidence interval of µ with confidence coefficient (1-α)

Describe in Detail

Obtain the sufficient statistics for the following distribution.

(i)

(ii)

Describe in Detail

Show that T ² statistic is invariant under changes in the unit of measurements for a p×1 random vector X of the form Y =C X + d where C is a p×p nonsingular matrix, d is a p×1 vector.

Describe in Detail

For a sequential probability ratio test of strength (α, β) and stopping bounds are A and B (B < A), show that A ≤ 1-β/α and B ≥ β/1-α

Describe in Detail

Let X= (X ₁, X ₂, X ₃) ’ be distributed as N ₃ (µ, ∑) where µ’= (2, -3, 1) and

(i) Find the distribution of 3X ₁ -2X ₂ +X ₃.

(ii) Find a 2 × 1 vector a such that X ₂ and are independent.