ICAR AIEEA PG Fisheries Science 14 July 2023 Shift-1 Paper

Karl Pearson's empirical relationship between mean, median, and mode for a moderately skewed unimodal distribution is:

Rearranging in terms of differences from the mean:

Given that $\text{Mean} - \text{Mode} = 36$:

Option analysis:

• $6$: Arithmetic miscalculation.
• $12$: Correct, calculated as $36 / 3 = 12$.
• $24$: Arithmetic miscalculation.
• $36$: Value of Mean - Mode, not Mean - Median.

Covariance is the fundamental statistical measure of the joint variability between two random variables, defined as $\text{Cov}(X,Y) = E[(X - E[X])(Y - E[Y])]$. It evaluates the extent to which two variables vary together. While correlation is the dimensionless, standardized measure of linear association (scaled between $-1$ and $+1$), covariance is the raw mathematical measure of joint co-movement.

Option analysis:

• Covariance: Correct, standard statistical definition for joint variability of two random variables.
• Correlation: Standardized covariance, measure of strength of linear relationship.
• Regression: Predicts the dependent variable from independent predictor(s).
• Coefficient of determination: $R^2$, proportion of variance explained by regression model.

The two draws from separate ponds are statistically independent events:

• Probability of drawing a marked fish from the first pond:
  $$P(A) = \frac{40}{200} = \frac{1}{5}$$
• Probability of drawing a marked fish from the second pond:
  $$P(B) = \frac{50}{300} = \frac{1}{6}$$
• Probability that both fishes are marked:
  $$P(A \cap B) = P(A) \times P(B) = \frac{1}{5} \times \frac{1}{6} = \frac{1}{30}$$
  
  Option analysis:
• $1/90$: Incorrect calculation.
• $1/60$: Incorrect calculation.
• $1/30$: Correct, $(1/5) \times (1/6) = 1/30$.
• $1/11$: Incorrect addition/ratio error.

Statement (I) is correct: Under UNCLOS Article 3, every coastal State has the right to establish the breadth of its territorial sea up to a limit not exceeding $12\text{ nautical miles}$ ($NM$) measured from baselines. Statement (II) is incorrect: Under UNCLOS Article 33, the contiguous zone may not extend beyond $24\text{ nautical miles}$ measured from the territorial BASELINES (not from the outer edge of the territorial sea). Thus, measured from the outer edge of the territorial sea, the contiguous zone spans a breadth of only $12\text{ NM}$ ($12$ to $24\text{ NM}$ from baseline).

Option analysis:

• Both correct: Incorrect because Statement II is false.
• Both incorrect: Incorrect because Statement I is true.
• Statement (I) is correct but Statement (II) is incorrect: Correct assessment.
• Statement (I) is incorrect: Incorrect because Statement I is true.