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Indian Mathematical Inequalities and Data Science

This quiz is designed to assess your knowledge of Indian mathematical inequalities and their applications in data science.

14 Questions Published
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Questions

Question 1 Multiple Choice (Single Answer)

Which of the following is an example of an Indian mathematical inequality?

  1. Cauchy-Schwarz inequality
  2. Jensen's inequality
  3. Chebyshev's inequality
  4. Markov's inequality
Question 2 Multiple Choice (Single Answer)

What is the statement of Jensen's inequality?

  1. If \(f\) is a convex function and \(X\) is a random variable, then \(E[f(X)] \ge f(E[X])\).
  2. If \(f\) is a concave function and \(X\) is a random variable, then \(E[f(X)] \le f(E[X])\).
  3. If \(f\) is a convex function and \(X\) is a random variable, then \(E[f(X)] \le f(E[X])\).
  4. If \(f\) is a concave function and \(X\) is a random variable, then \(E[f(X)] \ge f(E[X])\).
Question 3 Multiple Choice (Single Answer)

What is the statement of Chebyshev's inequality?

  1. For any random variable \(X\) with mean \(\mu\) and variance \(\sigma^2\), the probability that \(|X - \mu| \ge k\sigma\) is at most \(1/k^2\).
  2. For any random variable \(X\) with mean \(\mu\) and variance \(\sigma^2\), the probability that \(|X - \mu| \le k\sigma\) is at most \(1/k^2\).
  3. For any random variable \(X\) with mean \(\mu\) and variance \(\sigma^2\), the probability that \(|X - \mu| \ge k\sigma\) is at least \(1/k^2\).
  4. For any random variable \(X\) with mean \(\mu\) and variance \(\sigma^2\), the probability that \(|X - \mu| \le k\sigma\) is at least \(1/k^2\).
Question 4 Multiple Choice (Single Answer)

What is the statement of Markov's inequality?

  1. For any random variable \(X\) with mean \(\mu\) and variance \(\sigma^2\), the probability that \(|X - \mu| \ge k\sigma\) is at most \(1/k^2\).
  2. For any random variable \(X\) with mean \(\mu\) and variance \(\sigma^2\), the probability that \(|X - \mu| \le k\sigma\) is at most \(1/k^2\).
  3. For any random variable \(X\) with mean \(\mu\) and variance \(\sigma^2\), the probability that \(|X - \mu| \ge k\sigma\) is at least \(1/k^2\).
  4. For any random variable \(X\) with mean \(\mu\) and variance \(\sigma^2\), the probability that \(|X - \mu| \le k\sigma\) is at least \(1/k^2\).
Question 5 Multiple Choice (Single Answer)

Which of the following is an application of Jensen's inequality in data science?

  1. Risk minimization in machine learning
  2. Dimensionality reduction
  3. Clustering
  4. Classification
Question 6 Multiple Choice (Single Answer)

Which of the following is an application of Chebyshev's inequality in data science?

  1. Outlier detection
  2. Hypothesis testing
  3. Confidence intervals
  4. All of the above
Question 7 Multiple Choice (Single Answer)

Which of the following is an application of Markov's inequality in data science?

  1. Tail bounds
  2. Concentration inequalities
  3. Large deviations theory
  4. All of the above
Question 8 Multiple Choice (Single Answer)

Which of the following Indian mathematicians made significant contributions to the field of mathematical inequalities?

  1. Srinivasa Ramanujan
  2. Harish-Chandra
  3. C. R. Rao
  4. All of the above
Question 9 Multiple Choice (Single Answer)

What is the Rogers-Ramanujan identities?

  1. A set of 17 identities that relate the values of the Rogers-Ramanujan continued fraction at various arguments.
  2. A set of 17 identities that relate the values of the Rogers-Ramanujan continued fraction at various arguments.
  3. A set of 17 identities that relate the values of the Rogers-Ramanujan continued fraction at various arguments.
  4. A set of 17 identities that relate the values of the Rogers-Ramanujan continued fraction at various arguments.
Question 10 Multiple Choice (Single Answer)

What is the Ramanujan-Sato series?

  1. A series that expresses the Rogers-Ramanujan continued fraction as a sum of hypergeometric series.
  2. A series that expresses the Rogers-Ramanujan continued fraction as a sum of hypergeometric series.
  3. A series that expresses the Rogers-Ramanujan continued fraction as a sum of hypergeometric series.
  4. A series that expresses the Rogers-Ramanujan continued fraction as a sum of hypergeometric series.
Question 11 Multiple Choice (Single Answer)

What is the Harish-Chandra theory of harmonic analysis on semisimple Lie groups?

  1. A theory that studies the structure of semisimple Lie groups and their representations.
  2. A theory that studies the structure of semisimple Lie groups and their representations.
  3. A theory that studies the structure of semisimple Lie groups and their representations.
  4. A theory that studies the structure of semisimple Lie groups and their representations.
Question 12 Multiple Choice (Single Answer)

What is the Rao-Blackwell theorem?

  1. A theorem that states that the minimum variance unbiased estimator of a parameter is the conditional expectation of the parameter given the sufficient statistic.
  2. A theorem that states that the minimum variance unbiased estimator of a parameter is the conditional expectation of the parameter given the sufficient statistic.
  3. A theorem that states that the minimum variance unbiased estimator of a parameter is the conditional expectation of the parameter given the sufficient statistic.
  4. A theorem that states that the minimum variance unbiased estimator of a parameter is the conditional expectation of the parameter given the sufficient statistic.
Question 13 Multiple Choice (Single Answer)

What is the Cramér-Rao inequality?

  1. An inequality that provides a lower bound on the variance of any unbiased estimator of a parameter.
  2. An inequality that provides a lower bound on the variance of any unbiased estimator of a parameter.
  3. An inequality that provides a lower bound on the variance of any unbiased estimator of a parameter.
  4. An inequality that provides a lower bound on the variance of any unbiased estimator of a parameter.
Question 14 Multiple Choice (Single Answer)

Which of the following is an example of an Indian mathematical inequality that has been used in data science?

  1. The Cauchy-Schwarz inequality
  2. Jensen's inequality
  3. Chebyshev's inequality
  4. Markov's inequality
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