to Introduction Mathematical Statistics
Lecture 9 09-25-2007
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Announcements
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About the Quiz
Must remain 5 minutes. Schedule is tight. The problems will be posted on web before
the lecture.You get more time to work on it. Quiz will be closed book/lecture.
Show your work. No work, no credit. Solutions to quiz problems will be given
together with the homework solution per week.
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About the handouts
New handouts will have blank sheets for you
to take notes.
The lecture may cover some of the
homework problems - I may refuse to explain these problems during office hour.
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About the homework
Amount of homework will be reduced to
7-8 problems per week. through some of them.
Even problems only. But lecture will go Construction of the final grade will remain hw: 40%; quiz: 5%; midterm 1: 15%; midterm
2: 15%; Final: 25%
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About study group
Middlebush 11 has been reserved for
student study group, at Tuesday 5:00-7:00pm.
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About office hours
Tuesday: 2:00pm - 3:00pm Wednesday: 1:00 - 3:00pm
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About the schedule
Review session: Oct 23 Midterm 2: Oct 25 Review session: Dec 6 Office hour: Dec 11
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About Samsi workshop
SAMSI Undergraduate Workshop 11/9/2007 - 11/10/2007 (at SAMSI) 02/29/2008 - 03/01/2008 (SAMSI) 05/19/2008 - 05/23/2008 (NCSU) 07/21/2008 - 07/29/2008 (NCSU) Check the web:
http://www.samsi.info/programs/2007edoutreachprogram.shtml
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Tasks
Normal distribution Normal probability rule
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Normal distribution
Def. R.v. X is normal distribution, N( , 2
with mean and variance ), , if its density 1 is
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1 f (x) = exp(- 2 (x - )2 ). 2 2
It is also referred as Gaussian distribution.
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The m.g.f. is given by
respectively and
Show that the mean2and the variance are .
1 2 2 mx (t) = exp(t + t ) 2
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E.g. 4.1.1 (P114) Let X denote the number of
grams of hydrocarbons emitted by an automobile per mile. Assume that
Graph the density. Find the area corresponds to X > 1.5
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X N(1, 0.25 )
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E.g. A r.v.Y follows log-normal if Let Y denote the diameter in millimeters of P(Y > 2.7)?
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Y = e , X N(, ) .
X 2
Styrofoam pellets used in packing. Assume Y is log-normal with parameters 0.8 and 0.1.
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Standard normal distribution
Standard Normal: mean = 0, variance = 1. Let X N(, ), then
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X - N(0, 1).
The c.d.f. of standard normal is (x) .
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E.g.4.4.2 (P112) X: hydrocarbons emitted per
mile, X N(1, 0.252 ) .
What is the probability for (0.9 < X < 1.54)? Find out a value ...