6.4.2. Let X₁, X2,..., Xn and Y₁, Y2,..., Ym be independent random samples from N (01,03) and N(02, 04) distributions, respectively. (a) If C R³ is defined by Ω = = {(01,02,03): -∞ < 0₁ <∞, i = 1,2; 0 < 03 = 04 <∞0}, find the mles of 01, 02, and 03. (b) If NC R2 is defined by = {(01,03): -∞ < 0₁ = 0₂ <∞x; 0 < 03 = 04 <∞0},

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6.4.2. Let X₁, X2,..., Xn and Y₁, Y2,..., Ym be independent random samples from
N (01,03) and N(02, 04) distributions, respectively.
(a) If NC R³ is defined by
2= {(01,02,03): ∞ <0₂ <∞, i = 1,2; 0 < 03 = 04 <∞0},
find the mles of 01, 02, and 03.
(b) If NC R² is defined by
N = {(01,03): − ∞ < 0₁ = 0₂ < ∞; 0 < 03 = 04 <∞0},
find the mles of 0₁ and 03.
Transcribed Image Text:6.4.2. Let X₁, X2,..., Xn and Y₁, Y2,..., Ym be independent random samples from N (01,03) and N(02, 04) distributions, respectively. (a) If NC R³ is defined by 2= {(01,02,03): ∞ <0₂ <∞, i = 1,2; 0 < 03 = 04 <∞0}, find the mles of 01, 02, and 03. (b) If NC R² is defined by N = {(01,03): − ∞ < 0₁ = 0₂ < ∞; 0 < 03 = 04 <∞0}, find the mles of 0₁ and 03.
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