Unique College Of Computer Science & IT, Muzaffarabad
ass
HEALTH 5546chh

Summer 2016
STAB52, An Introduction to Probability  Tutorial 1
Danny Cao, 996979845
Department of Mathematics, University of Toronto
This tutorial focuses on one of the fundamental branches of applied probability theory: combinatorics.
To deal with any of the combin
Unique College Of Computer Science & IT, Muzaffarabad
ass
HEALTH 5546chh

Summer 2016
STAB52, An Introduction to Probability  Tutorial 9
Danny Cao, 996979845
Department of Mathematics, University of Toronto
First recall the that P(AB) = P(A B)/P(B) whenever P(B) > 0. That is, the probability of A given
B is the probability of A restricte
Unique College Of Computer Science & IT, Muzaffarabad
ass
HEALTH 5546chh

Summer 2016
STAB52, An Introduction to Probability  Tutorial 6 and 7
Danny Cao, 996979845
Department of Mathematics, University of Toronto
Definition: Given a random variable X, its cumulative distribution function is the function FX : R [0, 1]
defined by
FX (x) = P
Unique College Of Computer Science & IT, Muzaffarabad
ass
HEALTH 5546chh

Summer 2016
STAB52: Quiz1
[All relevant work must be shown for full credit]
Name:
Student number:
1) [6] A number is chosen at random from the set of numbers cfw_1, 2, 3, 1000. What is
the probability that it is divisible by 3 or 5 (divisible by 3 or 5 or both)?
Sol
Unique College Of Computer Science & IT, Muzaffarabad
ass
HEALTH 5546chh

Summer 2016
STAB52, An Introduction to Probability  Tutorial 8
Danny Cao, 996979845
Department of Mathematics, University of Toronto
Consider the set of numbers x1 , ., xn . Colloquially, the average of these values is understood to be
x
= (x1 + . + xn )/n. That is
Unique College Of Computer Science & IT, Muzaffarabad
ass
HEALTH 5546chh

Summer 2016
STAB52, An Introduction to Probability  Tutorial 2
Danny Cao, 996979845
Department of Mathematics, University of Toronto
We begin by discussing independence and conditional probability. Two events A and B are said to be
independent if P(A B) = P(A) P(B).
Unique College Of Computer Science & IT, Muzaffarabad
ass
HEALTH 5546chh

Summer 2016
STAB52, An Introduction to Probability  Tutorial 4
Danny Cao, 996979845
Department of Mathematics, University of Toronto
Definition: Given a random variable X, its cumulative distribution function is the function FX : R [0, 1]
defined by
FX (x) = P(X x).
Unique College Of Computer Science & IT, Muzaffarabad
ass
HEALTH 5546chh

Summer 2016
STAB52, An Introduction to Probability  Tutorial 3
Danny Cao, 996979845
Department of Mathematics, University of Toronto
In calculus, we consider functions which map the real number line to itself (namely, f : R R). In probability, the analogous concept
Unique College Of Computer Science & IT, Muzaffarabad
ass
HEALTH 5546chh

Summer 2016
STAB52, An Introduction to Probability  Tutorial 5
Danny Cao, 996979845
Department of Mathematics, University of Toronto
Given a random variable X, we are often interested in the new distribution
of X under some transfor
mation. For example, if X Poisson