For what is Basu's theorem often used?

To prove independence of two statistics

To measure the value of the statistics

To test the relationship between two statistical data sets

Where was Basu's theorem published?

Mahabharata - A Modern Retelling

Do You Know Basu's Theorem?

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| By Zlatan Aleksic

Zlatan Aleksic

Community Contributor

Quizzes Created: 206 | Total Attempts: 1,002,931

Questions: 10 | Attempts: 140 | Updated: Mar 22, 2023

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Basu's theorem gives new insights for statistics. After completing this test you will know how much you are familiar with Basu's theorem! Good luck and have fun whit this quiz!

Questions and Answers

1.

When was Basu's theorem created?
- A.
  
  1955
- B.
  
  1945
- C.
  
  1935
- D.
  
  1965
Correct Answer
A. 1955

Explanation
Basu's theorem was created in 1955.

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2.

What was the name of Basu's theorem creator?
- A.
  
  Subhash
- B.
  
  Debabrata
- C.
  
  Gopinath
- D.
  
  Santosh
Correct Answer
B. Debabrata

Explanation
Debabrata is the correct answer because the question asks for the name of the creator of Basu's theorem. Based on the given options, Debabrata is the only name that matches this criteria.

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3.

For what is Basu's theorem often used?
- A.
  
  To resolve statistics
- B.
  
  To measure the value of the statistics
- C.
  
  To prove independence of two statistics
- D.
  
  To test the relationship between two statistical data sets
Correct Answer
C. To prove independence of two statistics

Explanation
Basu's theorem is often used to prove the independence of two statistics. This theorem states that if a statistic is ancillary and sufficient, then it is independent of any other statistic that is based on the same sample. In other words, if two statistics are independent, it means that knowing the value of one does not provide any information about the other. Therefore, Basu's theorem is commonly employed to establish the independence between two statistics in statistical analysis.

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4.

With what other theorem independence of two statistics can also be proven?
- A.
  
  Theory of statistics
- B.
  
  Pell's theorem
- C.
  
  Probability theory
- D.
  
  Cochran's theorem
Correct Answer
D. Cochran's theorem

Explanation
Cochran's theorem is a statistical theorem that allows us to prove the independence of two statistics. It states that if two statistics are independently distributed under the null hypothesis, then their joint distribution is also independent. This theorem is commonly used in hypothesis testing and regression analysis to verify the independence of different statistical measures. Therefore, Cochran's theorem provides a reliable method to establish the independence of two statistics in the field of statistics.

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5.

Where was Basu's theorem published?
- A.
  
  Sankhya
- B.
  
  Mahabharata - A Modern Retelling
- C.
  
  Sanskrit for Seekers
- D.
  
  The Hitopadesa
Correct Answer
A. Sankhya

Explanation
Basu's theorem was published in the journal called Sankhya.

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1
0
6.

When was Debabrata Basu born?
- A.
  
  1916
- B.
  
  1924
- C.
  
  1942
- D.
  
  1961
Correct Answer
B. 1924

Explanation
Debabrata Basu was born in 1924.

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7.

What is proven in this example (See picture)?
- A.
  
  A is dependent of T
- B.
  
  A is independent of B
- C.
  
  A is independent of T
- D.
  
  B is independent of T
Correct Answer
C. A is independent of T

Explanation
The given example shows that A is independent of T. This means that the value or occurrence of A does not depend on the value or occurrence of T. In other words, T does not have any influence or impact on A.

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8.

In whos advanced texts the Basu's theorem makes appearance?
- A.
  
  Lehmann
- B.
  
  Mukhopadhyay
- C.
  
  Casella
- D.
  
  All of the above
Correct Answer
D. All of the above

Explanation
The Basu's theorem is discussed in advanced texts by Lehmann, Mukhopadhyay, and Casella. This theorem is a fundamental result in statistics that relates the sufficiency and ancillarity of a statistic.

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9.

With which scientist did Basu have intensive discussions in period when his theorem was developed?
- A.
  
  Abraham Wald
- B.
  
  Jerzy Neyman
- C.
  
  Egon Pearson
- D.
  
  Maurice George Kendall
Correct Answer
B. Jerzy Neyman

Explanation
Basu had intensive discussions with Jerzy Neyman during the period when his theorem was developed.

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10.

When was Basu elected for Fellow of the American Statistical Association?
- A.
  
  1985
- B.
  
  1989
- C.
  
  1979
- D.
  
  1963
Correct Answer
C. 1979

Explanation
Basu was elected as a Fellow of the American Statistical Association in 1979.

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