Chapter IV: Probability & Statistics
1. Sets
a. Find the union, intersection of sets, difference between two sets and the complement of
a set with respect to a universal set.
Resource: Example on slide (11-14) of IV-01
Homework (1): Ex (1) – (2)
b. Understand properties of sets, with special attention to De Morgan’s laws.
Resource: Example on slide (15) of IV-01
c. Understand the notions of disjoint and intersecting sets.
Resource: Example on slide (16) of IV-01
2. Finite Sets & Counting Principles
a. Understand and apply the formula for finding the number of elements of a union of two
sets
Resource: Examples (1) to (3) on slides (2 - 8) of IV-02
Homework (2): Ex (1) – (2)
b. Understand and apply the basic counting principle
Resource: Examples (4) to (6) on slides (10 - 14), Questions (1) to (4) on slides (15 –
18) of IV-02
Homework (2): Ex (3)
c. Understand the notion of permutation of n objects taken r at a time and use the
permutation formula correctly
Resource: Examples on slides (20), Example (7) on slide (21), Questions (5) to (6) on
slides (22 – 23) of IV-02
Homework (2): Ex (4)
Quiz (10)-Question (2)
d. Understand the notion of Permutations of n not all distinct objects taken n at a time and
use the permutation formula correctly
Resource: Example (8) on slide (25) of IV-02
Homework (2): Ex (4)
e. Understand the notion of combination of n objects taken r at a time and use the
combination formula correctly
Resource: Examples on slide (26), Example (9) on slide (27), Questions (7) on slide
(29) of IV-02
Homework (2): Ex (6)
1
Quiz (10)-Question (1)
3. Probability
a. Identify sample spaces
Resource: Example (1) to (2) on slides (4-5) of IV-03
b. Operation on events
Resource: Examples (3) on slide (9) of IV-03
c. Operation on events
Resource: Examples (3) on slide (9) of IV-03
d. Identifying events
Resource: Examples (4) to (7) on slides (10-20) of IV-03
e. Identifying events in sample spaces
Resource: Examples (4) to (7) on slides (10-20) of IV-03
f. Understand and apply the rules of probability and probability distribution
Resource: Examples (8) to (16) on slides (28-49) of IV-03
Homework (3): Ex (1) – (9)
Quiz (11)-Questions (1) & (2)
4. Conditional Probability
a. Find conditional probability or use its formula to find the probability of the intersection
Resource: Example (3) to (4) on slides (5-6) of IV-04
Homework (4): Ex (1)
Quiz (12)-Questions (1)
Interesting Examples: Example (1)
b. Understand and apply stochastic processes
Resource: Example (5)) on slides (8-10) of IV-04
Homework (4): Ex (2) Question (1)
c. Determine whether two or more events are independent
Resource: Example (6) to (7) on slides (12-13) of IV-04
Homework (4): Ex (3)
d. Understand & apply Bayes’ theorem
Resource: Example (8) to (10) on slides (242-33) of IV-04
Homework (4): Ex (4) – (6)
2
Quiz (12)-Questions (2)
Interesting Examples: Example (2)
5. Random Variable
a. Find values & type of a random variable
Resource: Example (1) to (3) on slides (3-9) of IV-05
Homework (5): Ex (1)
b. Find probability distribution and the histogram of a random variable
Resource: Example (4) to (6) on slides (12-19) and discussion on slides (20-27) of V05
Homework (5): Ex (2)
c. Find the mean of a group of numbers and the expected value of a random variable
Resource: Example (7) to (8) on slides (33-41) of V-05
Homework (5): Ex (3)
5. Odds, Median, Mode, Variance & Standard Variation
a. Find the odds in favor of an event given the probability of that event occurring and visa
versa
Resource: Example (1) to (2) on slides (4-6) of IV-06
Homework (6): Ex (1)
Quiz (13)-Questions (2)
b. Find the median and the mode of a group of numbers
Resource: Example (3) to (4) on slides (9-10) of IV-06
Homework (6): Ex (2)
c. Find the variance and the standard deviation of a random number
Resource: Example (5) to (6) on slides (17-21) of IV-06
Homework (6): Ex (3)
Quiz (13)-Questions (1)
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