Unit II: Random Variables and Mathematical Expectation
Random variable – discrete and continuous random variable – probability mass function and density function – distribution function and its properties – two dimensional random variables – joint probability mass and density function – marginal distribution function – conditional probability distribution – mathematical expectation and its properties – Moment generating function and its properties – central limit theorem (without proof).
Unit III: Probability Distributions
Discrete Probability distribution: Bernoulli distribution – Binomial distribution – Poisson distribution – Properties – their mean, variance and moment generating function. Continuous distribution: Normal, Standard normal distributions, Uniform, Exponential, Gamma, - Properties – their mean, variance and moment generating function.
Unit IV: Tests of Significance
Introduction – Parameter and statistic – Sampling Distribution – Standard Error – Null hypothesis and Alternative hypothesis – Level of significance and critical value – One Tailed and Two Tailed Tests – Type I and Type II errors – Test procedure. Large sample test – single mean and difference between two means – single proportion and difference between two proportions. Small sample tests – t-test for testing the significance of single mean – independent t-test (equal & unequal variances) and paired t test – chi square test for testing the association of a 2 x 2 contingency table.
Unit V: Statistical Quality Control
Introduction to Statistical Quality Control. Chance and assignable causes of variation – uses of Statistical quality control – process and product control - Control Charts and its uses – Control limits – control charts for variables-Construction of control charts for mean and range ( and R ) charts – control charts for attributes- ‘np’,‘p’ and C charts