2
A varietal trial on Wheat crop was conducted using a two-associate Partially Balanced Incomplete Block Design (PBIBD) with parameters $v = b = 9; r = k = 3; \lambda_1 = 1; \lambda_2 = 0; n_1 = 6; n_2 = 2$. In such a two-association scheme, the values of $p_{jk}^i$ written as matrices $P^1$ and $P^2$ are:
EXPLANATION
Incomplete Block Designs
- Associacy Matrices in Two-Associate Class PBIBD:
- In a two-associate PBIBD, parameters satisfy the identity relations:
- Given $n_1 = 6$ and $n_2 = 2$:
- For $P^1$ (first associates):
- Row 1: $p_{11}^1 + p_{12}^1 = 6 - 1 = 5 \implies 3 + 2 = 5$
- Row 2: $p_{21}^1 + p_{22}^1 = n_2 = 2 \implies 2 + 0 = 2$
- Hence, $P^1 = \begin{pmatrix} 3 & 2 \\ 2 & 0 \end{pmatrix}$
- For $P^2$ (second associates):
- Row 1: $p_{11}^2 + p_{12}^2 = n_1 = 6 \implies 6 + 0 = 6$
- Row 2: $p_{21}^2 + p_{22}^2 = n_2 - 1 = 2 - 1 = 1 \implies 0 + 1 = 1$
- Hence, $P^2 = \begin{pmatrix} 6 & 0 \\ 0 & 1 \end{pmatrix}$
- Conclusion: Matches Option 2.
Correct option: (2) ana p?= (5 ° 21 ol 2 as 4 ana p?= (¢ e 20 o1
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