Programme: BICTE Semester: Third
Course Title: Probability
and Statistics Nature of Course: Theory
Course Title: Math. Ed. 436 Credit Hour: 3
Total Period:48 hour Level: Bachelor’s Degree
1. Specific Objectives and Contents
|
Unit |
Objectives |
Contents |
|
I |
·
Define correlation and describe its types. ·
Interpret the different
values of r. ·
Compute Pearson's moment correlation and writes its properties |
Unit I:
Correlation (4) · Types of correlation · Computation of correlation coefficient (r)
and its interpretation, · Rank correlation, · Properties of correlation. |
|
II |
·
Define regression and
describe its types ·
Find the equation of regression and
its properties ·
Write the relation between
correlation and regression. |
Unit II:
Regression (6) ·
Types of relationship ·
Estimation of regression equations, ·
Properties of regression equations · Relationship between correlation and
regression. |
|
III |
·
Explain sample space, events, probability
of an event, Axioms of probability, ·
State and prove
Baye's theorem., ·
Define discrete random variables, probability
function, probability distributions, cumulative distribution, moments, mean,
and variance. ·
State uniform
distribution and write its properties ·
State Binomial
distributions and write their properties. ·
Define a continuous
random variable, probability density, cumulative density, mean and variance, ·
State and prove
Chebychev's inequality Describe laws of large numbers |
Unit III:
Probability Distribution (9) ·
Basic
terms of Probability. ·
Axioms and theorems of
probability ·
Conditional probability
& Baye's theorem. ·
Discrete random
variable, probability function, probability distributions, cumulative
distribution, moments, mean, and variance. ·
Uniform distribution
and its properties, ·
Binomial distributions
and their properties. ·
Continuous random
variable, probability density, cumulative density, mean, and variance. ·
Chebychev's inequality
and laws of large numbers. |
|
IV |
·
State normal
distributions and writes its properties. ·
Calculate the area
under the standard normal curves, Z score ·
Derive the normal approximations to the binomial distribution. |
Unit IV: Normal distributions (4) · Measure of Divergence from Normality · Properties: mean and variance, · Area under the standard normal curves · Z score |
|
V |
· Define parameters and statistics · Explain sampling distribution of the mean,
variance, standard error of statistics, and central limit theorem. · Define point and interval estimation. · State the properties of point estimation. · Compute the confidence
interval for mean and variance. |
Unit V: Sampling
Distribution and Estimation (8) · Parameter and statistics, sampling
distribution of mean/variance · Application of the central limit theorem ·
Estimation: Point estimation, interval estimation, ·
Confidence interval for mean and variance. |
|
VI |
·
Define null and alternate hypotheses. ·
Identify one-tailed, two-tailed
test, Type I, and Type II errors. ·
Set level of
significance and calculate critical region. ·
Identify test
statistics and describe sequential steps of hypothesis testing. ·
Solve test of hypothesis for the difference
between two means of large samples with unknown population variance. ·
Solve the Difference
between two means of small samples with unknown common variance, the significance
test of independence |
Unit VI: Test of Hypothesis (17) ·
Basic concepts. ·
Null/ Alternative hypothesis. ·
One-tailed / two-tailed tests ·
Type I /
Type II errors ·
Level of significance, Critical region, and Test
statistics ·
Steps in hypothesis testing. ·
Z-test: the difference between two means of large
samples with unknown population variance. ·
T-test: difference between two means of small
samples with unknown common variance. ·
Chi-square test: significance test of
independence. |
2. Course Description
This is an integrated course of probability and statistics for students with bachelor’s degrees in Information and Communication Technology (BICTE). This course provides a foundation for the students to understand the basic concept of mathematics to be applicable in the field of technology. The main aim of this course is to develop an in-depth understanding of different aspects of probability and statistics. This course covers correlation and regression, probability distributions, sampling distributions, estimation of parameters, and hypothesis testing.
3. General Objectives
The general objectives of this course are as follows:
· To impart practical knowledge and skills in deriving properties of correlation and regression and applying them to solve problems.
· To make the students familiar with random variables, and different discrete and continuous probability distributions.
· To make the students able to use sampling distribution and estimation of parameters, and use test of hypothesis in research work.
4.2 Specific Instructional Techniques
The specific teaching and learning techniques chapter
wise are listed below:
|
Unit |
Activity and Instructional Techniques |
Teaching Hours (48) |
|
I |
Lecture, discussion in group and question answer |
4 |
|
II |
Lecture, discussion in group and question answer |
6 |
|
III |
Lecture, discussion in group and question answer |
9 |
|
IV |
Lecture, discussion in group and question answer |
4 |
|
V |
Lecture, discussion in group and question answer |
8 |
|
VI |
Lecture, discussion in group and question answer |
17 |
5 Evaluation
5.1 Internal Evaluation
40%
Internal evaluation will be conducted by the subject teacher based
on the following aspects:
Attendance 4 marks
Participation in learning activities 6 marks
First assignment 10 marks
Second assignment 10 marks
Third assignment 10 marks
Total
40 marks
5.2 External Evaluation (60%)
The examination section Dean Office, Faculty of Education will
conduct the final examination at the end of the first semester. The type of
questions and marks allocated for each question will be as follows:
Objective type questions (multiple choice) 10 x 1 mark = 10
marks
Short answer questions 6 x 5 marks = 30
marks
Long answer questions 2
x 10 marks = 20 marks
Total
= 60
marks
6 Recommended
Books
Freund
J. E. (1997): Modern elementary Statistics, New Delhi: Prentice Hall of India
Garrett,
H. E. (). Statistics in psychology and
education. Longmans, NY: Green and Co. Inc.
Hayslett,
H. T (1983): Statistics Made Simple,
Heinemann: London
7. References
Mendenhall,
W, Scheaffer, R. L. and Wackerly, D. D. (1987): Mathematical Statistics with Applications. Boston: PWS Publishers.
Wallpole,
R. (1979): Introduction to Statistics,
Delhi: Macmillan, India
Pandit, R. P. and Bhattarai, L. N. (2016).
Mathematical Statistics, Kathmandu: Indira Pandit
Pandit Pandit, R. P. and Pahari, S.
(2016): Modern Elementary Mathematics,
Kathmandu: Indira Pandit
No comments:
Post a Comment