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```STAT 270
What’s going to be on the quiz
and/or the final exam?
Sampling Distribution of X
• Large samples, approx
N(, 
N(, 
• If population Normal,

n
)
)
n
• Small samples, population not normal,
 use simulation
unknown, unless can
• But why & when 
is this useful?
(
X - )
Sampling Distribution of X 1 -X 2
• Mean is 1- 2
1/ 2
(Var(X
)

Var(X
))
• SD is
1
2
^ ^  
• What about p1 - p2 ?
•Same but use short-cut formula for Var
of 0-1 population. (np(1-p))

Probability Models
• Discrete: Uniform, Bernoulli, Binomial,
Geometric, Negative Binomial,
Hypergeometric.
• Continuous: Uniform, Normal, Gamma,
Exponential, Chi-squared, Lognormal
• Poisson Process - continuous time and
discrete time approximations.
• Connections between models
• Applicability of each model
Probability Models - General
• pmf for discrete RV, pdf for cont’s RV
• cdf in terms of pmf, pdf, P(X…)
• Expected value E(X) - connection with
“mean”.
• Variance V(X) - connection with SD
• Parameter, statistic, estimator, estimate
• Random sampling, SWR, SWOR
Interval Estimation of
Parameters
• Confidence Intervals for population mean
– Normal population, SD known
– Normal population, SD unknown
– Any population, large sample
• Confidence Intervals for population SD
– Normal population (then use chi-squared)
• Confidence Level - how chosen?
Hypothesis Tests
• Rejection Region approach (like CI)
• P-value approach
(credibility assessment)
• General logic important …
– Problems with balancing Type I, II errors
– Decision Theory vs Credibility Assessment
– Problems with very big or small sample sizes
Applications
•
•
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•
•
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•
Portfolio of Risky Companies
Random Walk of Market Prices
Seasonal Gasoline Consumption
Car Insurance