# Mathematical Statistics by Ms. Iqra Liaqat

These notes are send by Ms. Iqra Liaqat. We are really very thankful to her for providing these notes and appreciates her effort to publish these notes on MathCity.org

Name | Mathematical Statistics |
---|---|

Provided by | Ms. Iqra Liaqat |

Pages | 298s pages |

Format | PDF (see Software section for PDF Reader) |

Size | 8 mB |

### Contents & Summary

In this section, the main heading are given below.

- Probability
- Mutually exclusive events
- Exhaustive events
- Equally likely events
- Counting rules
- Multiplication rule
- Permutation rule
- Combination rule
- Vote
- Classical definition of probability
- Relative frequency
- Subjective approach
- Axioms of probability
- General law of addition of probability
- Playing cards
- Condition al probability
- Multiplication law
- Total probability theorem
- Baye's theorem
- Random variable
- Distribution function
- Mean and variance of discrete random variable
- Continuous random variable
- Mean & variance of continuous random variable
- Chebyshev's inequality
- Joint Distribution
- Discrete probability distributions
- Uniform distribution
- Bernoulli trials
- Binomial experiment
- Properties of binomial experiment
- Binomial distribution
- Moments
- Moments generating function
- Cumulants
- Cumulants generating function (c.g.f)
- c.g.f of binomial distribution
- Hypergeometric distribution
- Properties of hypergeometric distribution
- Poisson distribution
- Properties of Poisson distribution
- Recurrence rule for Poisson probabilities
- Moment generating function
- Comulant generating function

- Central moment of Poisson distribution
- Negative binomial distribution
- Geometric distribution
- Continuous distributions
- Uniform distribution
- Exponential distribution
- Gauss distribution
- Beta function
- Beta distribution (1st kind)
- Beta distribution (2nd kind)
- Normal distribution (Gaussian distribution)
- Point of inflexion (inflection)
- Area under the normal curve
- Inverse normal distribution
- Normal approximation to binomial distribution
- Correction for continuity
- Normal approximation
- Normal approximation to Poisson distribution
- Properties of mathematical expectation
- Correlation
- Moments of uni-variate variable
- Moments of bi-variate variable
- Standardized covariance
- Regression
- Linear regression
- Method of least squares
- Regression lines
- Rank correlation
- Pearson product correlation formulas
- Derivation of rank correlation coefficient
- Rank correlation for tied ranks
- Coefficient of determination
- Standard error of estimates
- Multiple regression
- Deviation formulas
- Standard error of estimates
- Matrix representation
- Coefficient of multiple correlation and determination
- Multiple correlation an partial correlation
- Sampling and sampling distribution
- Standard error
- Sampling distribution
- Chi-square distribution
- Degree of freedom
- Properties of Chi-square distribution