MA7155 APPLIED PROBABILITY AND STATISTICS(Syllabus)(2013)

 UNIT I ONE DIMENSIONAL RANDOM VARIABLES

 Random variables - Probability function – Moments – Moment generating functions and their properties – Binomial, Poisson, Geometric, Uniform, Exponential, Gamma and Normal distributions – Functions of a Random Variable.

UNIT II TWO DIMENSIONAL RANDOM VARIABLES

Joint distributions – Marginal and Conditional distributions – Functions of two dimensional random variables – Regression Curve – Correlation.

UNIT III ESTIMATION THEORY

 Unbiased Estimators – Method of Moments – Maximum Likelihood Estimation - Curve fitting by Principle of least squares – Regression Lines.

UNIT IV TESTING OF HYPOTHESES

Sampling distributions - Type I and Type II errors - Testsbased on Normal, t, Chi-Square and F distributions for testing of mean, variance and proportions – Tests for Independence of attributes and Goodness of fit.

UNIT V MULTIVARIATE ANALYSIS

Random Vectors and Matrices - Mean vectors and Covariance matrices - Multivariate Normal density and its properties - Principal components Population principal components - Principal components from standardized variables.


 REFERENCES:

1. Jay L. Devore, “Probability and Statistics for Engineering and the Sciences”, Thomson and Duxbury, 2002.

2. Richard Johnson. ”Miller & Freund’s Probability and Statistics for Engineer”, Prentice – Hall, Seventh Edition, 2007.

3. Richard A. Johnson and Dean W. Wichern, “Applied Multivariate Statistical Analysis”, Pearson Education, Asia, Fifth Edition, 2002.

4. Gupta S.C. and Kapoor V.K.”Fundamentals of Mathematical Statistics”, Sultan and Sons, 2001. 5. Dallas E Johnson, “Applied Multivariate Methods for Data Analysis”, Thomson and Duxbury press, 1998.



MA7155 – Applied Probability and Statistics —  Download

MA7155 – Applied Probability and Statistics Question paper -- Download

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Important File Extensions

Zipped File 7z — 7-Zip compressed file gzip (.gz) — Compressed file .tar.gz, .tgz — gzipped tar file jar — ZIP file with manifest for use with Java applications RAR Rar Archive (.rar) — for multiple file archive (rar to .r01-.r99 to s01 and so on) zip — popular compression format   Desktop publishing .indd - Adobe InDesign .psd - Adobe Photoshop .pdf - Adobe Acrobat or Adobe Reader .qxd - QuarkXPress Document /Spreadsheet Files .xl - Excel Spreadsheet .xlr - Works Spreadsheet .xlsx - Microsoft Excel Open XML Spreadsheet .log - Log File .odt - OpenDocument Text Document .pages - Pages Document .doc - Microsoft Word Document .docx - Microsoft Word Open XML Document .tex - LaTeX Source Document .wps - Microsoft Works Word Processor Document .msg - Outlook Mail Message .rtf - Rich Text Format File .txt -   Plain Text File  .vcf -   vCard File .dat -   Data File .pptx -   PowerPoint Open XML Presentation .sdf -   Standard Data File .csv  -   Comma Seperated Values File .xml -   XML File .pps -   PowerPoint Slide Show .ppt  -   PowerPoint Presentation   Audio Files .aif   -   Audio Interchange File Format .mpa  -   MPEG-2 Audio File .ra  -   Real Audio File .iff  -   Interchange File Format .wav  -   WAVE Audio File .wma  -   Windows Media Audio File .mp3  -   MP3 Audio File   Video Files .avi  -  Audio Video Interleave File .3gp  -  3GPP Multimedia File .flv  -  Flash Video File .mpg  -  MPEG Video File .vob  -  DVD Video Object File .mp4  -  MPEG-4 Video File .3g2  -  3GPP2 Multimedia File .m4v  -  iTunes Video File .wmv  -  Windows Media Video File .swf  -  ShockWave Flash   Image Files .gif   -  Graphical Interchange Format File .jpg  -  JPEG Image .bmp  -  Bitmap Image File .psd   -  Adobe Photoshop Document .png  -  Portable Network Graphic .jpg  -  JPEG Image (Full form is Joint Photographic Experts Group)   Database Files .mdf - Microsoft SQL Server Database .sql - bundled SQL queries .pdb  -  Program Database .dbf  -  Database File .accdb  -  Access 2007 Database File .db   -  Database File .sql  -  Structured Query Language Data File .mdb  -  Microsoft Access Database   Executable Files .exe  - Windows Executable File .bat  - DOS Batch File   Programe/Code Files .cgi  - Common Gateway Interface Script .vb  - VBScript File .cs  - C Sharp file .jar  - Java Archive File .bat  - DOS Batch File .aspx  - Asp.net Extension .asp  - Active Server Page .php  - PHP Source Code File .cpp   - C++ Source Code File .c    - C/C++ Source Code File   Web Files .cer  - Internet Security Certificate .css  - Cascading Style Sheet .html   - Hypertext Markup Language File .js  - JavaScript File .jsp  - Java Server Page .htm  - Hypertext Markup Language File .xhtml  - Extensible Hypertext Markup Language File .rss   - Really Simple Syndication   Other Files .tmp   - Temporary File .bak   - Backup File .cab - cabinet file

Basic Concepts of hardware

Memory in Computers and Disks / Drives

There are several different types of memory:

· RAM (random-access memory): This is also known as main memory.  Computers can write and read data from RAM.   This is in contrast to ROM  which permits you only to read data.  However, most RAM is volatile, which means that it requires a steady flow of electricity to maintain its contents.  As soon as the power is turned off, whatever data was in RAM is lost. The users access data in RAM memory randomly as per needs.  RAM can be erased or written over at will by the computer programme

· ROM (read-only memory):  Computers almost always contain a small amount of read-only memory, commonly known as ROM.  This memory holds instructions for starting up the computer. As name indicates you can only read from this memory and cannot write anything on it.  Moreover, it is non-volatile in nature  i.e. even when power is switched off, the memory is not lost.

Thus, we can say that RAM is like a slate where you can write something for immediate reference and then wipe / change data by adding or deleting when it is not needed, but ROM is like a printed book, where once the text is  printed then it cannot be altered.

· PROM (programmable read-only memory): A PROM is a memory chip on which you can store a  programme.. But once the PROM has been used, you cannot wipe it clean and use it to store something else. Like ROMs, PROMs are non-volatile.

· EPROM (erasable programmable read-only memory): An EPROM is a special type of PROM that can be erased by exposing it to ultraviolet light.

· EEPROM (electrically erasable programmable read-only memory):An EEPROM is a special type of PROM that can be erased by exposing it to an electrical charge.

Memory is measured in bytes.  A byte is usually made up of 8 bits and represents one character - a letter, digit or symbol.   The number of bytes that can be held is a measure of the memory and storage capacity.   Bytes are usually measured in groups of kilobytes, megabytes, gigabytes and terabytes. 

Disk Drives

Secondary memory is also known as external memory or storage.  It consists of Hard Discs,   Floppy Disc (now a days out of fashion) , CDs  and DVDs  as well as pen drives.  External device consists of more storage space and most dynamic in terms of storing data. 
The disk drive determines the path by which you send and receive information to the computer. Information stored on a disk is measured in bytes.   We have already explained the methods used to represent bytes

1. a : drive is  popularly known as floppy drive as it was usually reserved for the floppy disks.  Floppy disk or diskette used to comes in two basic sizes; 5.25 inch and 3.5 inch. Both have a low and high density versions though 3.5 inch high density disks are the most common. However, now a days most of the PCs do not have this drive as floppy has become obsolete.   The later date diskettes that were inserted into the a: drive were 3 ½ inch size which could hold 1.44 megabyte of information.   Initially these disk had to be formatted before being put to use, but later on  pre-formatted disks were available. Formatting prepares the disk to be written upon. Diskettes can also be write-protected. This prevents you from writing on the disk. To write-protect a disk, slide the corner tab to uncover the opening.

2. c: drive is popularly reserved for the hard disk drive in computers   It is a thick Frisbee-like disk inside the computer, which can hold considerable higher  information than a diskette. The hard disk drive reads and stores information faster than the a: drive.  The memory size of these hard disks has greatly enhanced in last few years.

3. d: drive is mostly used for CD-ROM i.e. for playing the CDs .  CDs are inserted into this drive. A CD can contain more information than 100 diskettes. Computers are not able to write to the CD-ROM drive unless a CD Burner is present. The CD-ROM drives read information at various speeds.  However, sometimes d: drive is a part of the Hard Disk as such disks are partitioned into more than one segment where c:,  d:  and even e: are used for hard disk which has been partitioned.

In addition to above standard features for drives, now a days :

4. Some computers today come equipped with a zip drive. A zip drive provides additional storage space. A zip disk is inserted into the zip drive. The zip disk can hold 100 megabytes of information. Zip drives can be attached to an existing computer.

5. DVD (Digital Versatile Disc) drive is a new technology that stores more information than a CD-ROM and can be written upon. A DVD disk is inserted into this drive. The drive may come built into the computer or may be attached. These disk often are used to store movies or interactive video games. The disk resembles a CD but has 7 times the storage capacity.

6. Pen Drives are now popular and may be shown as e: or f: drives.   These are used to store data which needs to be carried somewhere else.

Disk size	Amount of storage	Approximate printed  8.5 x 11 inch pages
3.5 high density	1.44 Mb	720 pages
CD	650 Mb	a small library
DVD	4.5 Gb	a feature length movie
DVD dual layer	8 Gb	a long feature length movie with extras

Methods Used for Reading of Memory :

Sequential access refers to reading or writing data records in sequential order, that is, one record after the other. To read record 10, for example, you would first need to read records 1 through 9. This differs from random access, in which you can read and write records in any order.    Some programming languages and operating systems distinguish between sequential-access data files and random-access data files, allowing you to choose between the two types.   Sequential-access files are faster if you always access records in the same order. Random-access files are faster if you need to read or write records in a random order.

Devices can also be classified as sequential access or random access. For example, a tape drive is a sequential-access device because to get to point q on the tape, the drive needs to pass through points a through p.    The disk drive, on the other hand, is a random-access devicebecause the drive can  access any point on the disk without passing through all intervening points.

MODEM  :  Full form of modem is MOdulator and DEModulator. The modem is a converter of analog to digital and digital to analog.  Thus, we can say that a modem is a mechanical means of translating computer information or retrieving information from the Internet via a phone line.  It needs communication software in order to work and can be attached internally or externally.   Internet transmission can also take place over an ISDN line or the even faster T1 line. No modem is necessary for these types of transmission but you will need an ISDN adapter. Modems are measured by the speed that the information is transferred. The measuring tool is called the baud rate. Originally modems worked at speeds below 2400 baud but today analog speeds of 56,000 are standard. Cable, wireless or digital subscriber lines can transfer information much faster with rates of 300,000 baud and up.