18ProbDistRelation

# 18ProbDistRelation - Statistical Techniques I EXST7005...

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Statistical Techniques I EXST7005 Probability distribution interrelationships

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≠ ≥ ≤ μαβτεδχσ± √∼ ∞f8e5 ¹³£mabtedcs±Ö~¥`
Probability Distribution interrelationships The probability tables we have been examining are interrelated. One of these interrelationships is actually pretty important!

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Probability Distribution interrelationships (continued) The distributions are 1) Z = (Y- μ )/ σ = ( f8e5 Y- μ )/ σf8e5 Y = ( f8e5 Y- μ )/( σ / n) 2) χ 2 = Z2 with 1 d.f. χ 2 = Σ Z2 with n d.f. χ 2 = SS/ σ 2 with n-1 d.f. 3) t = (Y- μ )/S = ( f8e5 Y- μ )/S f8e5 Y = ( f8e5 Y- μ )/(S/ n) with n 1 d.f. 4) F = S12 / S22 with n1-1, n2-1 d.f.
Interrelationships 1) χ 2/ γ with γ d.f. = F with γ , ∞ d.f. since χ 2/ γ = (SS/ σ 2)/ γ (1/ γ / 1 /γ ) = SS/ ( γ σ 2) (1/ γ / 1 /γ ) = (SS/ γ )/ σ 2 = S2/ σ 2 which follows an F distribution with γ , ∞ d.f.

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Interrelationships (continued) 2) F = χ 12/
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## This note was uploaded on 12/29/2011 for the course EXST 7087 taught by Professor Wang,j during the Fall '08 term at LSU.

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18ProbDistRelation - Statistical Techniques I EXST7005...

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