# Probability and Statistics (3130006)

## Teaching Scheme (in Hours)

Theory Tutorial Practical Total
3 2 0 5

Subject Credit :  5

Theory
ESE (E)
Theory
PA (M)
Practical
ESE Viva (V)
Practical
PA (I)
Total
70 30 0 0 100

## Syllabus Content

###### Unit-1:  Basic Probability

Experiment, definition of probability, conditional probability, independent events, Bayes' rule, Bernoulli trials, Random variables, discrete random variable, probability mass function, continuous random variable, probability density function, cumulative distribution function, properties of cumulative distribution function, Two dimensional random variables and their distribution functions, Marginal probability function, Independent random variables.

###### Unit-2:  Some special Probability Distributions

Binomial distribution, Poisson distribution, Poisson approximation to the binomial distribution, Normal, Exponential and Gamma densities, Evaluation of statistical parameters for these distributions

###### Unit-3:  Basic Statistics

Measure of central tendency: Moments, Expectation, dispersion, skewness, kurtosis, expected value of two dimensional random variable, Linear Correlation, correlation coefficient, rank correlation coefficient, Regression, Bounds on probability, Chebyshev‘s Inequality

###### Unit-4:  Applied Statistics

Formation of Hypothesis, Test of significance: Large sample test for single proportion, Difference of proportions, Single mean, Difference of means, and Difference of standard deviations. Test of significance for Small samples: t- Test for single mean, difference of means, t-test for correlation coefficients, F- test for ratio of variances, Chi-square test for goodness of fit and independence of attributes.

###### Unit-5:  Curve fitting by the numerical method

Curve fitting by of method of least squares, fitting of straight lines, second degree parabola and more general curves

## Course Outcome

• Understand the terminologies of basic probability, two types of random variables and their probability functions
• Observe and analyze the behavior of various discrete and continuous probability distributions
• Understand the central tendency, correlation and correlation coefficient and also regression
• Apply the statistics for testing the significance of the given large and small sample data by using t- test, F- test and Chi-square test
• Understand the fitting of various curves by method of least square

### BE (CE) ⇒ Semester: 3

Darshan Institute of Engineering & Technology is a leading institute offering undergraduate (B.E.), postgraduate (M.E.) and Diploma programs in engineering.

## Our Contacts

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