CHi square,T and F-distribution

Question 1

Define canonical definition of central Chi-square distribution.

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Question 2

What is degree of freedom?

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Question 3

What is the definition of a Chi-square distribution?

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Question 4

pdf of Chi-square distribution

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Question 5

derive the expression for pdf of Chi-square distribution

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Question 6

derive the mean and variance of chi square distribution

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Question 7

what is the mean and variance of chi- square distribution

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Question 8

derive the mode or modal value of chi square distribution

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Question 9

show the additive property of chi-square variate

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Question 10

show the recurrence relation for the moments of chi-square distribution

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Question 11

write the expansion of log(1-x)

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Question 12

show the limiting behaviour of chi-square distn when n tends to infinity.

Answer 12

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Question 13

what is the mgf. of standard normal variate?

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Question 14

what is the definition of Fisher’s t-distribution?

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Question 15

Derive the expression for Fisher t-statistics.

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Question 16

derive the mean and variation for Fisher t distribution.

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Question 17

derive the expression for moments of t-distribution.

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Question 18

derive the mgf. of t-distribution.

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Question 19

derive the recurrence relation of t-distribution.

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Question 20

derive the expression for mean deviation of t-distribution.

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Question 21

Derive the limiting form of t-distribution.

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Question 22

Show that student t statistic is special case of Fisher t statistic.

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Question 23

what is the formula for Stirling approximation?

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Question 24

Define F-Statistic.

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Question 25

Derive the expression for the pdf of F-distribution.

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Question 26

Explain the role of coordinate transformation in deriving the pdf of t and f distribution.

Answer 26

Fill out the satisfactory correct answer.

Question 27

Write three different forms of Beta integral.

Answer 27

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Question 28

show that for F distribution:
mode exists only if m > 2.
Mode is always lesser than unity.
mean is always greater than unity.

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Question 29

Derive the modal value and mode for F-distribution.

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