Question:
Let \( (X_1, Y_1), (X_2, Y_2), \ldots, (X_{20}, Y_{20}) \) be a random sample from the \( N_2(0, 0, 1, 1, \frac{3}{4}) \) distribution. Define
\[\bar{X} = \frac{1}{20} \sum_{i=1}^{20} X_i \quad \text{and} \quad \bar{Y} = \frac{1}{20} \sum_{i=1}^{20} Y_i.\]
Then \( \text{Var}(\bar{X} - \bar{Y}) \) is equal to:
Let \( (X_1, Y_1), (X_2, Y_2), \ldots, (X_{20}, Y_{20}) \) be a random sample from the \( N_2(0, 0, 1, 1, \frac{3}{4}) \) distribution. Define
\[\bar{X} = \frac{1}{20} \sum_{i=1}^{20} X_i \quad \text{and} \quad \bar{Y} = \frac{1}{20} \sum_{i=1}^{20} Y_i.\]
Then \( \text{Var}(\bar{X} - \bar{Y}) \) is equal to:
\[\bar{X} = \frac{1}{20} \sum_{i=1}^{20} X_i \quad \text{and} \quad \bar{Y} = \frac{1}{20} \sum_{i=1}^{20} Y_i.\]
Then \( \text{Var}(\bar{X} - \bar{Y}) \) is equal to:
Updated On: Oct 1, 2024
- \( \frac{1}{16} \)
- \( \frac{1}{40} \)
- \( \frac{1}{10} \)
- \( \frac{3}{40} \)
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The Correct Option is B
Solution and Explanation
The correct option is (B): \( \frac{1}{40} \)
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