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Let's analyze each of the statements to determine which one is true:

1. **Statement (a):** "If more training data are taken, then the variance increases."
   - **False.** Generally, when more training data are used, the variance decreases. Variance in statistical models refers to how much the predictions for a given data point fluctuate based on different training sets. More data typically leads to more stable models, reducing variance.

2. **Statement (b):** "If more training data are taken, then the variance decreases."
   - **True.** As more training data are used, the model tends to generalize better, and the variance in predictions typically decreases.

3. **Statement (c):** "If Bias is 1 then it is called an unbiased estimator."
   - **False.** An estimator is called "unbiased" if its expected value equals the true value of the parameter being estimated, meaning the bias is 0. If the bias is 1, it cannot be called unbiased.

4. **Statement (d):** "If the variance of an estimator is maximum compared to any other estimator of the same parameter and it is unbiased, then it is called the minimum variance unbiased estimator."
   - **False.** The minimum variance unbiased estimator (MVUE) is the unbiased estimator that has the **least** variance among all unbiased estimators, not the maximum.

### Conclusion: 
The correct statement is **(b)**: "If more training data are taken, then the variance decreases."

Would you like more details or have any questions?

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Here are 5 related questions to expand on this topic:
1. What is the relationship between bias and variance in machine learning?
2. How does increasing the number of data points affect bias in a model?
3. What is the bias-variance tradeoff in statistical models?
4. What are some examples of minimum variance unbiased estimators (MVUE)?
5. How does variance differ from standard deviation in the context of estimators?

**Tip:** In machine learning, balancing bias and variance is crucial for creating models that generalize well to unseen data.

Which of the following statement is true?
(a) If more training data are taken, then the variance increases.
(b) If more training data are taken, then the variance decreases.
(c) If Bias is 1 then it is called unbiased estimator.
(d) If variance of an estimator is maximum to any other estimator of the same parameter and it is unbiased then it is called minimum variance unbiased estimator.

Learn about the bias-variance tradeoff and minimum variance unbiased estimators (MVUE) in this detailed explanation. Understand why more training data decreases variance and why unbiased estimators are important in statistical modeling.

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