Mathematical Probability 1 (MATS2105)
Mathematics and Computer Science - MCS
Semester: First Semester
Level: 200
Year: 2017
1
University of Bamenda
Faculty of Science
Department of Mathematics and Computer Science
Continuous Assessment
Course Title: Mathematical Probability I.
Course Code : MAT2105.
Duration: 2 hrs.
Course Instructor: Bime Markdonal. G
Instructions: Answer all questions. You are reminded of the necessity for good English and orderly
presentation of your answers.
1.
(a) (2 Marks) Define a probability measure
(b) (3+3 Marks) Let Ω be a sample space, A , B ⊂ Ω and ℙ a probability measure. Show
that
i.
ℙ ( A
C
) = 1 - ℙ (A)
ii.
I f A ⊂ B , then ℙ ( A ) ≤ ℙ ( B)
2.
(i+3+4+3 Marks) Let X be a random variable.
(a)
Define E ( X ) , the expectation of X .
(b)
X is said to have poission distribution with parameter > 0 if
ℙ
−
=
!
, = 0,1,2 …
i.
Show that
!
, is indeed a probability mass function.
ii.
Show that if X follows a poission distribution with parameter > 0, then E ( X ) = λ.
iii.
Compute ℙ (X > 2) when X has poission distribution with parameter 3
3.
(1+3+3 Marks) Let A , B be events. What does it mean to say A and B are independent?
Suppose A and B are independent. Show that
(a)
A
c
and B are independent
(b)
A
c
and B
c
are also independent
4.
(4 Marks) Suppose that we have four Maths books, five Language books and two arts
books which we want to put on a shelve. If we put them in a completely random order,
what is the probability that the books are grouped per subject?
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