Stats 241.3 Term Test 4

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Stats 241.3 Term Test 4

• Solutions

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c)
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d)
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• An alternative solution is to use the probability
  mass function

and
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Probabilityhas many applications in many areas

• Medicine
• Modeling epidemics
• Modeling disease progression
• Engineering
• Reliability design electrical systems
• Economics
• Modeling of financial time series, economic time
  series
• Determining Risk

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Statistics
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What is Statistics?

• It is the major mathematical tool of scientific
  inference methods for drawing conclusion from
  data.
• Data that is to some extent corrupted by some
  component of random variation (random noise)

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Phenomena
Non-deterministic

• Deterministic

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Deterministic Phenomena

• A mathematical model exists that allows accurate
  prediction of outcomes of the phenomena (or
  observations taken from the phenomena)

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Non-deterministic Phenomena

• Lack of perfect predictability

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Non-deterministic Phenomena
Random

• haphazard

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Random Phenomena

• No mathematical model exists that allows accurate
  prediction of outcomes of the phenomena (or
  observations)
• However the outcomes (or observations) exhibit in
  the long run on the average statistical
  regularity

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• In both Statistics and Probability theory we are
  concerned with studying random phenomena

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In probability theory

• The model is known and we are interested in
  predicting the outcomes and observations of the
  phenomena.

outcomes and observations
model
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In statistics

• The model is unknown
• the outcomes and observations of the phenomena
  have been observed.
• We are interested in determining the model from
  the observations

outcomes and observations
model
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Example - Probability

• A coin is tossed n 100 times
• We are interested in the observation, X, the
  number of times the coin is a head.
• Assuming the coin is balanced (i.e. p the
  probability of a head ½.)

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Example - Statistics

• We are interested in the success rate, p, of a
  new surgical procedure.
• The procedure is performed n 100 times.
• X, the number of successful times the procedure
  is performed is 82.
• The success rate p is unknown.

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• If the success rate p was known.
• Then

This equation allows us to predict the value of
the observation, X.
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• In the case when the success rate p was unknown.
• Then the following equation is still true the
  success rate

We will want to use the value of the observation,
X 82 to make a decision regarding the value of
p.
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Introductory Statistics Courses Non calculus
BasedStats 244.3 Stats 245.3Calculus Based
Stats 242.3
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Stats 244.3 Statistical concepts and techniques i
ncluding graphing of distributions, measures of 
location and variability, measures of association
, regression, probability, confidence intervals
, hypothesis testing. Students should consult wi
th their department before enrolling in this cour
se to determine the status of this course in
their program. Prerequisite(s)A course in a soc
ial science or Mathematics A30. 
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Stats 245.3An introduction to basic statistical 
methods including frequency distributions, elemen
tary probability, confidence intervals and tests o
f significance, analysis of variance, regression 
and correlation, contingency tables, goodness of 
fit. Prerequisite(s)MATH 100, 101, 102, 110 or 
STAT 103. 
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Stats 242.3Sampling theory, estimation, confidenc
e intervals, testing hypotheses, goodness of fit,
 analysis of variance, regression and correlatio
n. Prerequisite(s)MATH 110, 116 and STAT 241. 
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• Stats 244 and 245
• do not require a calculus prerequisite
• are Recipe courses
• Stats 242
• does require calculus and probability (Stats 241)
  as a prerequisite
• More theoretical class You learn techniques for
  developing statistical procedures and thoroughly
  investigating the properties of these procedures

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Statistics Courses beyond Stats 242.3
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• STAT 341.3
• Probability and Stochastic Processes 1/2(3L-1P)
  Prerequisite(s) STAT 241. Random variables
  and their distributions independence moments
  and moment generating functions conditional
  probability Markov chains stationary
  time-series.

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• STAT 342.3
• Mathematical Statistics 1(3L-1P)
  Prerequisite(s) MATH 225 or 276 STAT 241 and
  242. Probability spaces conditional
  probability and independence discrete and
  continuous random variables standard probability
  models expectations moment generating
  functions sums and functions of random
  variables sampling distributions asymptotic
  distributions. Deals with basic probability
  concepts at a moderately rigorous level.Note
  Students with credit for STAT 340 may not take
  this course for credit.

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• STAT 344.3
• Applied Regression Analysis 1/2(3L-1P)
  Prerequisite(s) STAT 242 or 245 or 246 or a
  comparable course in statistics. Applied
  regression analysis involving the extensive use
  of computer software. Includes linear
  regression multiple regression stepwise
  methods residual analysis robustness
  considerations multicollinearity biased
  procedures non-linear regression.Note Students
  with credit for ECON 404 may not take this course
  for credit. Students with credit for STAT 344
  will receive only half credit for ECON 404.

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• STAT 345.3
• Design and Analysis of Experiments 1/2(3L-1P)
  Prerequisite(s) STAT 242 or 245 or 246 or a
  comparable course in statistics. An
  introduction to the principles of experimental
  design and analysis of variance. Includes
  randomization, blocking, factorial experiments,
  confounding, random effects, analysis of
  covariance. Emphasis will be on fundamental
  principles and data analysis techniques rather
  than on mathematical theory.

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• STAT 346.3
• Multivariate Analysis 1/2(3L-1P)
  Prerequisite(s) MATH 266, STAT 241, and 344 or
  345. The multivariate normal distribution,
  multivariate analysis of variance, discriminant
  analysis, classification procedures, multiple
  covariance analysis, factor analysis, computer
  applications.

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• STAT 347.3
• Non Parametric Methods 1/2(3L-1P)
  Prerequisite(s) STAT 242 or 245 or 246 or a
  comparable course in statistics. An
  introduction to the ideas and techniques of
  non-parametric analysis. Includes one, two and K
  samples problems, goodness of fit tests,
  randomness tests, and correlation and regression.

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• STAT 348.3
• Sampling Techniques 1/2(3L-1P) Prerequisite(s)
  STAT 242 or 245 or 246 or a comparable course in
  statistics. Theory and applications of sampling
  from finite populations. Includes simple random
  sampling, stratified random sampling, cluster
  sampling, systematic sampling, probability
  proportionate to size sampling, and the
  difference, ratio and regression methods of
  estimation.

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• STAT 349.3
• Time Series Analysis 1/2(3L-1P)
  Prerequisite(s) STAT 241, and 344 or 345. An
  introduction to statistical time series analysis.
  Includes trend analysis, seasonal variation,
  stationary and non-stationary time series models,
  serial correlation, forecasting and regression
  analysis of time series data.

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• STAT 442.3
• Statistical Inference 2(3L-1P) Prerequisite(s)
  STAT 342. Parametric estimation, maximum
  likelihood estimators, unbiased estimators,
  UMVUE, confidence intervals and regions, tests of
  hypotheses, Neyman Pearson Lemma, generalized
  likelihood ratio tests, chi-square tests, Bayes
  estimators.

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• STAT 443.3
• Linear Statistical Models 2(3L-1P)
  Prerequisite(s) MATH 266, STAT 342, and 344 or
  345. A rigorous examination of the general
  linear model using vector space theory. Includes
  generalized inverses orthogonal projections
  quadratic forms Gauss-Markov theorem and its
  generalizations BLUE estimators Non-full rank
  models estimability considerations.