# PROBABILITY and STATISTICS

## TOPICS OF PROBABILITY and STATISTICS

➣Understanding Data

➣Data Collection and Uni-variate Distributions

➣Exploring Bivariate Distributions

➣Probability

➣Discrete Probability Distributions

➣Continuous Probability Distributions

➣Multivariate Probability Distributions

➣Sampling Distributions, and Control Charts

➣Estimation

➣Hypothesis Testing

➣Inference for Regression Parameters

➣ANOVA

## TRAINING HIGHLIGHTS

➣The training curriculum is designed to prepare the participants to explore Univariate, Bivariate and Multivariate Probability distributions and tasks such as Hypothesis Testing.

➣Participants will be provided enough examples and illustrations to analyze and perform ANOVA

➣Usage of Real Time Example and Case study provide confidence to the participants

➣Data from one or more areas of interest will be taken as a case study and a detailed analysis is performed

➣All calculations and analysis are done using MS EXCEL 2010 or SPSS. The spread sheets/data files used for the training will be shared with the participants.

➣The course is participative

## PRE REQUISITES

Participants are not expected to have any Statistical knowledge as this training starts from the basic.

## DETAILED COURSE content

## TOPICS covered

Methods of Data Collection | Planning and Conducting Surveys | Planning and Conducting Experiments | Planning and Conducting an Observational Study |

Types of Data | Frequency Distribution Tables | Graphical Methods | Tools for Describing Data: Numerical Measures |

Summary Measures and Decisions | Two-Way Table for Categorical Data | Scatterplots | Correlation |

Regression: Modeling Linear Relationships | Fitting the model: The least-squares approach | Using the model for prediction | Coefficient of Determination |

Residual Analysis | Transformations | Definition of Probability | Counting Rules Useful in Probability |

Conditional Probability and Independence | Rules of Probability | Odds and Odds Ratios | Random Variables and Their Probability Distributions |

Expected Values of Random Variables | Bernoulli Distribution | Binomial Distribution | Geometric and Negative Binomial Distributions |

Poisson Distribution | Hypergeometric Distribution | Moment-Generating Function | Simulating Probability Distributions |

Continuous Random Variables and Their Probability Distributions | Expected Values of Continuous Random Variables | Uniform Distribution | Exponential Distribution |

Gamma Distribution | Normal Distribution | Lognormal Distribution | Beta Distribution |

Weibull Distribution | Reliability | Moment-Generating Functions for Continuous Random Variables | Simulating Probability Distributions |

Bivariate and Marginal Probability Distributions | Conditional Probability Distributions | Independent Random Variables | Expected Values of Functions of Random Variables |

Multinomial Distribution | More on the Moment-Generating Function | Conditional Expectations | Sampling Distribution of X-bar |

Sampling Distribution of Sample Proportion Y/N | Sampling Distributions: The Multiple-Sample Case | Control Charts | Process Capability |

Point Estimators and Their Properties | Confidence Intervals: The Single-Sample Case | Confidence Intervals: The Multiple Samples Case | Prediction Intervals |

Tolerance Intervals | Method Of Maximum Likelihood | Terminology | Hypothesis Testing: The Single-Sample Case |

Multiple-Sample Case | Chi-Squared Tests on Frequency Data | Goodness of Fit Tests | Acceptance Sampling |

Regression Models with One Predictor Variable | Probability Distribution of the Random Error Component | Making Inferences about Slope | Linear Model for Estimation and Prediction |

Multiple Regression Analysis | Inference in Multiple Regression | Model Building: A Test for a Portion of a Model | Other Regression Models |

Checking Conditions and Some Pitfalls | Review of Designed Experiments | Analysis of Variance (ANOVA) Technique | Completely Randomized Design |

Relation of ANOVA for CRD with a t-Test | Relation of ANOVA for CRD with a Regression | Analysis of Variance for the Randomized Block Design | Factorial Experiment |