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Exponential Distribution

•   T  ∼ Exp (λ)

•   Probability density function

f  (t) =  λe−λt

for  t > 0

•   Cumulative distribution function

F  (t) = 1 − e−λt

for  t > 0

•   E [T ] =   1λ

•   V ar (T ) =   1λ2

Distributions

• Assume that the population distribution is normal with mean  µ  and variance σ2

•   Then

χ2n−1 =

 (n − 1) s2

σ2

Hypothesis testing

•   Overall Significance

F   =  SSR/K 

SSE/ (n − K − 1),

where K is the number of independent variables and n is the number of observations. Reject  H 0   if 

F > F K,n−K −1,α

• Complete Model v.s. Restricted Model

F  = (SS E (Restricted) − SS E ) /R

s2e,

where R is the number of additional independent variables. Reject H 0   is  F > F R,n−K −R−1,α

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Figure 1: Standard Normal Distribution

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Figure 2: F Distribution Table4

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Figure 3: Student t Distribution Table

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