## Statistics and Probability

Subject Code |
Subject Name |
Credits |
||||||||||||

MCA105 |
Statistics And Probability |
04 |
||||||||||||

Subject
Code |
Subject Name | Teaching
Scheme |
Credits
Assigned |
|||||||||||

Theory | Pract | Tut | Theory | TW | Tut. | Total | ||||||||

MCA105 |
Statistics And Probability |
04 |
— |
— |
04 |
— |
— |
04 |
||||||

Subject Code | Subject Name | Examination Scheme | ||||||||||||

MCA 105 |
Statistics And Probability |
Theory Marks | TW | Pract | Oral | Total | ||||||||

Internal Assessment | End Semester Exam | |||||||||||||

Test1 (T1) | Test2 (T2) | Average of T1 & T2 | ||||||||||||

20 | 20 | 20 | 80 | – | – | – | 100 | |||||||

** ****Pre-requisites:**

Basic Mathematics, combinatorics and calculus Knowledge.

## Course Educational Objectives (CEO):

CEO 1 |
To equip the students with a working knowledge of probability, statistics, and modeling in the presence of uncertainties. |

CEO 2 |
To understand the concept of hypothesis and significance tests |

CEO 3 |
To help the students to develop an intuition and an interest for random phenomena and to introduce both theoretical issues and applications that may be useful in real life. |

**Course Outcomes: At the end of the course, the students will be able to:**

MCA105.1 |
Distinguish between quantitative and categorical data |

MCA105.2 |
Apply different statistical measures on data |

MCA105.3 |
Identify, formulate and solve problems |

MCA105.4 |
Classify different types of Probability and their fundamental applications |

**Syllabus**

Sr. No |
Module |
Detailed Contents |
Hours |

1 |
Measures of Central Tendency &Measures of Dispersion |
Frequency Distribution, Histogram, Stem and leaf diagram, ogives, Frequency Polygon, Mean, Median, Mode, Range, Quartile Deviation, Mean Deviation, Box whisker plot, Standard Deviation, Coefficient of Variation | 8 |

2 |
Skewness, Correlation & Regression |
Karl Pearson‟s coefficient of Skewness, Bowley‟s coefficient of Skewness, Scatter Diagram, Karl Pearson‟s coefficient of correlation, Spearman‟s rank correlation coefficient , Linear Regression and Estimation, Coefficients of regression | 8 |

3 |
Theory of Attributes |
Classes and Class Frequencies, Consistency of Data, Independence of Attributes, Association of Attributes | 4 |

4 |
Testing of Hypothesis |
Hypothesis, Type I and Type II errors. Tests of significance
– Student’s t-test:Single Mean, Difference of means, paired t-test, Chi-Square test:Test of Goodness of Fit, Independence Test |
10 |

5 |
Introduction to Probability |
Random experiment, Sample space, Events, Axiomatic Probability, Algebra of events | 4 |

6 |
Conditional Probability |
Conditional Probability, Multiplication theorem of Probability, Independent events, Baye‟s Theorem | 6 |

7 |
Random variables |
Discrete random variable, Continuous random variable, Two-dimensional random variable, Joint probability distribution, Stochastic independence | 7 |

8 |
Mathematical Expectation |
Expected value of a random variable, Expected value of a function of a random variable,Properties of Expectation and Variance, Covariance | 5 |

** **

**Reference Books:**

** **

- Fundamentals of Mathematical Statistics – 1st Edition S.C.Gupta, V.K.Kapoor , S Chand
- Introduction to Probability & Statistics – 4th Edition J.Susan Milton, Jesse C. Arnold Tata McGraw Hill
- Fundamentals of Statistics : 7th edition S C Gupta, Himalaya Publishing house
- Probability and Statistics with Reliability, Queuing, And Computer Science Applications (English) 1st Edition: Kishore Trivedi, PHI
- Schaum‟s Outlines Probability, Random Variables & Random Process 3rd Edition Tata

McGraw Hill

- Probability & Statistics for Engineers: Dr J Ravichandran, Wiley
- Statistics for Business and Economics: Dr Seema Sharma, Wiley
- Applied Business Statistics 7th Edition Ken Black, Wiley