Bioinformatics- ICAR JRF/SRF 2024

• Probability of Independent Events:
• Probability of husband's selection: $P(H) = \frac{1}{7} \implies P(H^c) = 1 - \frac{1}{7} = \frac{6}{7}$
• Probability of wife's selection: $P(W) = \frac{1}{5} \implies P(W^c) = 1 - \frac{1}{5} = \frac{4}{5}$
• Since the two selection decisions are independent:
• Case 1: Husband selected and Wife not selected: $P(H \cap W^c) = P(H) \times P(W^c) = \frac{1}{7} \times \frac{4}{5} = \frac{4}{35}$
• Case 2: Husband not selected and Wife selected: $P(H^c \cap W) = P(H^c) \times P(W) = \frac{6}{7} \times \frac{1}{5} = \frac{6}{35}$
• Probability that only one of them will be selected:

• Conclusion: The probability is 2/7 (Option 1).

Correct option: (1) 27

• Matching Probability Distributions with Properties:
• Binomial Distribution $\to$ (IV): Models the number of successes $k$ in $n$ independent Bernoulli trials with constant success probability $p$.
• Normal Distribution $\to$ (II): Continuous symmetric bell-shaped distribution completely characterized by parameters $\mu$ and $\sigma$.
• Poisson Distribution $\to$ (III): Discrete distribution that models count of rare independent events occurring within a specified interval of time, area, or volume.
• Chi-Square Distribution $\to$ (I): Non-negative distribution fundamental to tests of goodness-of-fit and contingency table tests of independence in categorical data analysis.
• Matching Result: (A) - (IV), (B) - (II), (C) - (III), (D) - (I) (Option 4).

Correct option: (4) (A) - (IV), (B) - (IID, (C) - (ID, (B) - (1)

• Properties of Sampling Distributions:
• A sampling distribution is the probability distribution of a given sample statistic (such as sample mean $\bar{x}$ or sample proportion $p$) obtained through repeated sampling from a population. (True)
• By the Central Limit Theorem (CLT), as sample size $n$ increases, the sampling distribution of the sample mean approaches a normal distribution regardless of the underlying population shape. (True)
• The standard deviation of the sampling distribution of the sample mean (standard error) is $\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}$, which is strictly smaller than the population standard deviation $\sigma$ for $n \gt 1$. (False)
• Sampling distributions provide the theoretical basis for constructing confidence intervals and conducting hypothesis tests to estimate population parameters. (True)
• Conclusion: Statements (A), (B) and (D) only are true (Option 2).

Correct option: (2) (A), (B) and (D) only,

• Heritability and Resemblance Between Relatives:
• Assertion (A): The correlation between relatives helps estimate heritability in quantitative genetics. $\implies$ True.
• Resemblance between relatives (parent-offspring regression, full-sib or half-sib intraclass correlations) allows partitioning of phenotypic variance to estimate narrow-sense ($h^2$) and broad-sense ($H^2$) heritability.
• Reason (R): Heritability is the proportion of phenotypic variance due to genetic and environmental variance. $\implies$ False.
• Heritability is the proportion of total phenotypic variance attributable to genetic variance alone ($H^2 = V_G / V_P$, or $h^2 = V_A / V_P$), not the sum of genetic and environmental variances ($V_P = V_G + V_E$).
• Conclusion: (A) is true but (R) is false (Option 3).

Correct option: (3) (A) is true but (R) is false

• Breeding Value in Quantitative Genetics:
• The Breeding Value ($A$) of an individual is defined as the value of an individual judged by the mean performance of its progeny.
• It reflects the additive genetic effect transmitted from parent to offspring through individual gametes, representing the expected contribution of that individual's genotype to the phenotype of its offspring.
• Conclusion: The expected contribution of that individual's genotype to the phenotype of its offspring (Option 2).

Correct option: (2) The expected contribution of that individual's genotype to the phenotype of its offspring