STA257
Probability & Statistics I-Fall, 2013
Welcome to STA257 . This is an introductory mathematical statistics
course with an emphasis on probability.
Necessary background: You must
be taking, or have taken and passed, a 2nd year calculus course as well
as 2nd year linear algebra. Students
not having this background should consider other alternative
courses. Please do not attempt this course without the necessary
background. With very few exceptions, it is very unwise to do so.
Course
Outline: Course outline including marking scheme.
Lectures Detailed lectures,
relevent text sections, suggested problems, class notes ( scribbles for
your convenience only). Not all items covered in class are here. The
detailed lectures contain material
not covered in class. You are responsible it.You may make an audio
recording of the lectures given in class. This may be important as not
everything said will be written down.
Instructor Office Hours:
After
class,
e-mail,
by
appointment.
Office=SS5016H, e-mail =
philip@utstat.toronto.edu .
Tutorials will begin the 2nd
week of classes. Tutorial rooms will be
posted the 2nd week on Blackboard.
Special TA office hours
will be held before the test and the final exam. Times will be posted
on Blackboard.
Test Date: Wed, Oct 16 from
7-10PM
and Test Location: SS2110
and the lecture room. See Blackboard for your room.
Practice
test This should give you a good idea as to what
the test will be like. It will be live by 7PM on the Tuesday before the
test. Now Live.
Coverage: Roughly
lectures 1-
5
as given in class and on the web, the practice test and all suggested
problems. In addition please do the following problems.
Extra important problems:
1. Let events An increase to A. Find A and show P(An
) -> P(A). Show the same thing in the decreasing case. Use these
results to show that a df F is right continuous, F(oo)=1, F(-oo)=0.
2. Let X be exponential(2). Calculate the df, mgf and variance. Sketch
the df.
3. Let X have pdf f(x)=c/x2 , x>1 and is 0 otherwise.
Find c. Calculate the first 2 moments.
4. Let X be standard exponential. Show P(X>s+t)=P(X>t|X>s),
for all s,t>0. This is the ageless or memoryless property. Show this
also holds for the geometric(p) if we require s,t to be positive
integers.