# Probability & Statistics for GTU 18 Course (III - ECE/CSE/IT - 3130006) & GTU 20 Course (CSE(AI & ML- 3130006))

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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. Mar!Jinal probability function. Independent random variables. (Chapter- 1) 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. (Chapter- 2) 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, Re!Jression. Bounds οη probability, Chebyshev's Inequality. (Chapter- 3) 4. Applied Statistics: Formation of Hypothesis. Test of si!Jnificance : Lar!Je sample test for sin!Jle proportion. Difference of proportions. Sin!Jle mean. Difference of means. and Difference of standard deviations. Test of si!Jnificance for Small samples: t- Test for sin!Jle mean. difference of means. t-test for correlation coefficients, F- test for ratio of variances. Chi-square test for !Joodness of fit and independence of attributes. (Chapter- 4) 5. Curve fitting by the numerical method: Curve fittin!J by of method of least squares. fittin!J of strai!Jht lines. second de!Jree parabola and more !Jeneral curves. (Chapter- 5)

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