Agricultural Statistics- ICAR JRF/SRF 2024

• Hardy-Weinberg Equilibrium Genotype Frequencies:
• For a diallelic gene with allele frequencies $p$ (allele $A$) and $q$ (allele $a$) such that $p + q = 1$:
• Heterozygote frequency: $f(Aa) = 2pq$
• Recessive homozygote frequency: $f(aa) = q^2$
• Given condition: The heterozygous genotype is twice as frequent as the homozygous recessive genotype:

• Dividing both sides by $2q$ (for $q \neq 0$):

• Since $p + q = 1$ and $p = q$:

• Conclusion: The required allelic frequencies are p = 0.5; q = 0.5 (Option 4).

Correct option: (4) p=05;q=05

• Correlation vs. Independence in Standard Normal Variables:
• Given $X \sim N(0, 1)$ and $Y = X^2$:
• The Pearson correlation coefficient is given by:

• For a standard normal distribution:
• $E[X] = 0$
• $E[XY] = E[X \cdot X^2] = E[X^3]$
• Since the standard normal distribution is symmetric about 0, all its odd central moments are zero:

• Therefore, the covariance is:

• Consequently, $\rho(X, Y) = 0$.
• Key Insight: A correlation coefficient of 0 indicates absence of linear association, even though $X$ and $Y$ have a perfect non-linear functional dependence ($Y = X^2$) (Option 2).

Correct option: (2) 0

• Testcross Phenotypes for a Polyhybrid Genotype:
• Genotype of the individual: $AaBbCcDd$ (heterozygous at $n = 4$ independently assorting gene loci).
• Testcross involves crossing with a homozygous recessive tester: $AaBbCcDd \times aabbccdd$.
• For each independent gene locus under complete dominance, the testcross produces 2 phenotypic classes:
• $Aa \times aa \to 1\,A\_ : 1\,aa$ (2 phenotypes)
• $Bb \times bb \to 1\,B\_ : 1\,bb$ (2 phenotypes)
• $Cc \times cc \to 1\,C\_ : 1\,cc$ (2 phenotypes)
• $Dd \times dd \to 1\,D\_ : 1\,dd$ (2 phenotypes)
• Total number of distinct phenotypic classes in the testcross progeny is:

• Conclusion: 16 distinct phenotypes appear in the testcross progeny (Option 1).

Correct option: (1) 16