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COURSE OBJECTIVES: ᧢ To develop Probability techniques in manufacturing and quality evaluation process. ᧢ To acquaint the knowledge of testing of hypothesis for small and large samples which plays an important role in real life problems. UNIT I PROBABILITY AND RANDOM VARIABLES 9 Axioms of probability - Conditional probability - Total probability - Baye᧙s theorem- Discrete and continuous random variables ᧓ Moments. UNIT II STANDARD DISTRIBUTIONS 9 Binomial ᧓ Poisson ᧓ Exponential ᧓ Normal distributions ᧓ Moment generating functions and their properties. UNI*******WO DIMENSIONAL RANDOM VARIABLES 9 Joint distributions ᧓ Marginal and conditional distributions ᧓ Covariance ᧓ Correlation and linear regression ᧓ Central limit theorem(Statement only). UNIT IV TESTING OF HYPOTHESIS 9 Sampling distributions ᧓ Statistical hypothesis ᧓ Tests for single mean, proportion, Difference of means (large and small samples) ᧓ Tests for single variance and equality of variances ᧓ Chi square test for goodness of fit-Independence of attributes. UNIT V DESIGN OF EXPERIMENTS 9 One way and two way classifications ᧓ Completely randomized design ᧓ Randomized block design ᧓ Latin square design. L:45 T:0 P: 0 Total: 45 Periods TEXT BOOKS T1 Ibe, O.C., ᧜Fundamentals of Applied Probability and Random Processes᧝, Elsevier, 1st Indian Reprint, 2016. T2 Papoulis, A and Unnikrishnapillai, S., ᧜Probability, Random Variables and Stochastic Processes᧝ McGraw Hill Education India, 4th Edition, New Delhi, 2010. REFERENCES R1 Walpole. R.E., Myers. R.H., Myers. S.L., and Ye. K., ᧜Probability and Statistics for Engineers and Scientists᧝,9th Edition, Pearson Education, Asia, 2010. R2 Trivedi, K.S., ᧜Probability and Statistics with Reliability, Queuing and Computer Science Applications᧝, PHI Learning Private limited , New Delhi ,2011. R3 Devore. J.L., "Probability and Statistics for Engineering and the Sciences", Cengage Learning, New Delhi, 8 th Edition, 2014. R4 Ross, S.M., ᧜Introduction to Probability and Statistics for Engineers and Scientists᧝, 3rd Edition, Elsevier, 2004. R5 Spiegel,M.R., Schiller, J. and Srinivasan,R.A., "Schaum᧙s Outlines on Probability and Statistics᧝, Tata McGraw Hill edition, 4th Edition, 2012.
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23MAT206-PROBABILITY AND STATISTICS

1. Binomial Distribution in Medical Diagnosis Systems(CSE-1-20 and BME-1-20)

Study how Binomial Distribution is used to calculate the probability of successful disease detection in AI-based healthcare systems.

Relevant for:

  • CSE ᔒ Machine Learning, Predictive Analytics
  • BME ᔒ Medical Testing and Diagnosis

2. Poisson Distribution in Hospital Emergency Management

(CSE-21-40 and BME-21-40)

Analyze patient arrival rates in emergency wards using Poisson Distribution and discuss how it helps in hospital resource planning.

Relevant for:

  • CSE ᔒ Data Analysis, Simulation
  • BME ᔒ Healthcare Operations

3. Normal Distribution in Human Health Data

(CSE-41-68 and BME-41-60)

Investigate how Normal Distribution is applied to blood pressure, heart rate, BMI, or glucose level analysis.

Relevant for:

  • CSE ᔒ Health Data Visualization
  • BME ᔒ Biomedical Signal Interpretation
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