Utkal University, Odisha, Mathematics Semester 5, Probability and Statistics Syllabus

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Unit - 1 Probability

Unit 1

Probability

1.1 Probability Introduction Sample spaces Events probability of events rules of probability

1.2 Conditional probability Independent events

1.4 Bayes’s theorem

1.3 Probability distributions and probability densities random variables probability distributions continuous random variables probability density functions

1.4 Multivariate distributions joint distribution function

1.5 Joint probability density function marginal distributions

1.6 Conditional distributions conditional density

1.7 The theory in practice data analysis frequency distribution class limits class frequencies class boundary class interval class mark skewed data multimodality graphical representation of the data measures of location and variability

1.8 Population sample parameter

Unit - 2 Mathematical Expectation

Unit 2

Mathematical Expectation

2.1 Mathematical Expectation Introduction expected value of random variable

2.2 Moments Chebyshev’s theorem

2.3 Moment generating functions Product moments

2.4 Moments of linear combinations of random variables

2.5 Conditional expectation

2.6 The theory in practice measures of Location dispersion

Unit - 3 Special Probability Distributions

Unit 3

Special probability distributions

3.1 Special probability distributions Discrete Uniform distribution

3.2 Binomial distribution

3.3 Negative binomial Geometric Hypergeometric distributions

3.5 Poisson multinomial distribution

3.6 Multinomial Special probability densities

3.7 Uniform distribution exponential gamma chisquare beta distribution

3.8 Normal normal approximation to binomial

3.9 Bivariate normal

3.10 Functions of random variables

3.11 Distribution function technique transformation techniqueone variable several variables moment generating function technique

Unit - 4 Sampling Distributions

Unit 4

Sampling distributions

4.1 Sampling distributions population distribution random sample sampling distribution of mean

4.2 Central Limit theorem

4.3 Sampling distribution of the mean finite populations

4.4 Chisquare t F distributions

4.5 Regression and correlation Bivariate regression regression equation Linear Regression

4.6 Method of least squares

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Other Subjects of Semester-5
Linear algebra
Linear programming
Multivariate calculus
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