CHi square,T and F-distribution Flashcards
Define canonical definition of central Chi-square distribution.
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What is degree of freedom?
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What is the definition of a Chi-square distribution?
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pdf of Chi-square distribution
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derive the expression for pdf of Chi-square distribution
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derive the mean and variance of chi square distribution
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what is the mean and variance of chi- square distribution
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derive the mode or modal value of chi square distribution
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show the additive property of chi-square variate
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show the recurrence relation for the moments of chi-square distribution
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write the expansion of log(1-x)
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show the limiting behaviour of chi-square distn when n tends to infinity.
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what is the mgf. of standard normal variate?
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what is the definition of Fisher’s t-distribution?
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Derive the expression for Fisher t-statistics.
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derive the mean and variation for Fisher t distribution.
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derive the expression for moments of t-distribution.
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derive the mgf. of t-distribution.
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derive the recurrence relation of t-distribution.
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derive the expression for mean deviation of t-distribution.
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Derive the limiting form of t-distribution.
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Show that student t statistic is special case of Fisher t statistic.
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what is the formula for Stirling approximation?
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Define F-Statistic.
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Derive the expression for the pdf of F-distribution.
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Explain the role of coordinate transformation in deriving the pdf of t and f distribution.
Fill out the satisfactory correct answer.
Write three different forms of Beta integral.
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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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Derive the modal value and mode for F-distribution.
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