MTH3111 Probability and Statistics

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MTH-3111Probability and Statistics

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Course details

• Instructor Dr. Mohamed H. Hassan
• Office Deputy Dean (Academic Affairs).
• Phone 4411
• mhhassan_at_iiu.edu.my
• Course 3 credits, 3 Lecture hours, 1 hours
  tutoring (Sign up sheet for tutorials).
• Text Applied Statistics and Probability for
  Engineers, D. C. Montgomery and G. C. Runger, 3rd
  edition, John Wiley Sons, Inc.

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Course details

• Quiz during tutorial from assignment problems
• Changing of Quiz grades can only be done during
  the first week after getting the grades.
• Course outline lecture notes are posted on
• http//eng.iiu.edu.my/mhassan/MTH-3111

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Dress code in attending classes

• Matric card must always be displayed.
• No round neck shirt.
• No slippers.
• No tight pants or shirt.
• No long hair for brothers (cap should be removed
  while in the classroom)

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Learning outcomes

• After completing this course, the student should
  be able to
• Define sample space and event and calculate
  probability calculation of an event, conditional
  probability and total probability.
• Define probability mass function and cumulative
  distribution function.
• Apply Binomial, Poisson, exponential and normal
  distribution for modelling empirical phenomenon.
• Understand and use Central Limit Theorem to find
  sampling distribution of mean and use it to find
  interval estimation.
• Define hypothesis testing and to calculate the
  test statistic for mean of a normal distribution,
  p-value, type I error, type II error, and power
  of a test statistic.
• Find linear regression estimator by using least
  squares method and make and analyse a simple
  design of experiment.

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Introduction
The Engineering method for problem solving
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Introduction (Cont.)

• Engineers must know how to efficiently plan
  experiments, collect data, analyze and interpret
  the data, and understand how the observed data
  are related to the model they have proposed for
  the problem under study.
• Statistics Deals with the collection,
  presentation, analysis, and use of data to make
  decisions, solve problems, and design products
  and processes.

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Variability

• Variability Successive observations of a system
  or phenomena do not produce exactly the same
  result.
• Statistical methods are used to help us describe
  and understand variability. It also can give us
  a useful way to incorporate this variability into
  our decision-making processes.

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Variability (examples)

• Car gasoline mileage performance
• Observed variability in gasoline mileage depends
  on many factors (sources of variability), such as
  the type of driving, vehicle condition, the
  brand and/or octane number of the gasoline used,
  weather conditions.
• Statistics gives us a framework for describing
  this variability and for learning about which
  potential sources of variability are the most
  important or which have the greatest impact on
  the gasoline mileage performance.

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Variability (examples)

• Designing a nylon connector to be used in an
  automotive engine application.
• We specify design specification on wall
  thickness, and determine effect on the connector
  pull-off force.
• Eight prototype units are produced and their
  pull-off forces measured. Not all of the
  prototypes have the same pull-off force.
• We say that there is variability in the pull-off
  force measurements. THUS, we consider the
  pull-off force to be a random variable.
• We often need to describe, quantify and
  ultimately reduce variability.

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Data collecting methods

• Basic methods of collecting data
• A retrospective study using historical data
• An observational study
• A designed experiment
• An effective data collection procedure can
  greatly simplify the analysis and lead to
  improved understanding of the population or
  process that is being studied.

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Retrospective study

• A retrospective study would use either all or a
  sample of the historical process data archived
  over some period of time.
• It presents some problems Data didnt change
  much over the historical period. Effects of
  process variables may be difficult to separate.

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Observational Study

• The engineer observes the process or population,
  disturbing it as little as possible, and records
  the quantities of interest.
• Because these studies are usually conducted for a
  relatively short time period, sometimes variables
  that are not routinely measured can be included.
  It goes a long way toward obtaining accurate and
  reliable data.
• STILL, Effects of process variables may be
  difficult to separate.

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Designed Experiments

• The engineer makes deliberate or purposeful
  changes in the controllable variables of the
  system or process, observes the resulting system
  output data, and then makes an inference or
  decision about which variables are responsible
  for the observed changes in output performance.
• With designed experiments
• Products and processes enjoy better performance,
  higher reliability, and lower overall costs.
• They play a crucial role in reducing the lead
  time for engineering design and development
  activities.

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Statistical inference