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C3_W3_Quiz.md

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1. What is the difference between sample mean and population mean?

  • Sample mean is the average of a subset of the population, while population mean is the average of the entire population.
  • Sample mean is always smaller than population mean.
  • There is no difference between sample mean and population mean.

2. Which of the following method can be used to estimate the variance, mean, and proportion of a population?

  • Sample mean
  • Sample variance
  • Point estimation
  • Regression analysis

3. Which of the following statements best describes the law of large numbers?

  • The law of large numbers states that as the sample size increases, the sample mean becomes more variable.
  • The law of large numbers states that as the sample size increases, the sample mean approaches the population mean with increasing accuracy.
  • The law of large numbers states that as the sample size increases, the sample variance approaches the population variance.
  • The law of large numbers states that as the sample size increases, the sample becomes more biased.

4. Suppose you flip a coin 10 times and obtain 6 heads and 4 tails. What function needs to be maximized to find the maximum likelihood estimate of the probability of getting heads on a single coin toss? Let $p$ be the probability of the coin being heads.

  • $L \left( p \right) = p^{1/6} \left( 1- p \right)^{1/4}$
  • $L \left( p \right) = p^{6} \left( 1- p \right)^{4}$
  • $L \left( p \right) = p^{4} \left( 1- p \right)^{6}$
  • $L \left( p \right) = p^{10} \left( 1- p \right)^{0}$

5. What is the porpose of regularization in machine learning?

  • Regularization is used to make a model more complex and flexible, which can lead to better performance on the training data.
  • Regularization is used to prevent overfitting and reduce the complexity of a model, by adding a penalty term to the loss function that encourages smaller parameter values.
  • Regularization is used to increase the training error of a model, which can improve its generalization performance.
  • Regularization is used to improve the interpretability of a model by reducing its complexity.

6. Consider the following population: $\left[ -2, -1, 0, 1, 2 \right]$ and the following sample $\left[ -1, 0, 2 \right]$.

What is the population mean?

Answer: 0

7. Consider the following population: $\left[ -2, -1, 0, 1, 2 \right]$ and the following sample $\left[ -1, 0, 2 \right]$.

What is the sample variance? (Use two decimal places in your answer)

Answer: 2.33