Teaching CSIR NET Mock Test Series Mathematical Science Statistics & Exploratory Data Analysis Independent Random Variables
For n ≥ 2, let ϵ1, ϵ2, ..., ϵn be independent and identically distributed (i.i.d.) N(0, σ2) random variables and
Yi = i α + i2 α2 + ϵi, i = 1, ..., n,
where σ > 0 and α ∈ ℝ are unknown parameters. Then which of the following is a jointly minimal sufficient statistic for (α, σ) ?
1
\((\sum_{i=1}^n Y_i^2, \sum_{i=1}^n i Y_i, \sum_{i=1}^n i^2 Y_i)\)
2
\((\sum_{i=1}^n Y_i^2, \sum_{i=1}^n i Y_i, \sum_{i=1}^n i^2 Y_i^2)\)
3
\((\sum_{i=1}^n i Y_i, \sum_{i=1}^n i^2 Y_i^2)\)
4
\((\sum_{i=1}^n Y_i, \sum_{i=1}^n i Y_i)\)