# 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 |

Note - Course content and topics to be covered in the training can be customized as per requirement for Corporates.

## Faculty profile

## FEES for Corporates

Based on the syllabus, contents and other requirements for the corporate training, scope with detailed inclusions and exclusions along with the fee will be shared. There will be a 14% service tax over and above the training fee.