Integral Calculus: Advanced Applications to Mathematical Statistics · Introduction

Introduction

What this guide covers

An exhaustive tour of the formalization of continuous probability theory, exponential moments, multivariate transformations and analytical marginalization.

Overview

Topics covered

Introduction
Applications to Mathematical Statistics
Fundamentals of Continuous Probability and Integration
1.1 Probability Density Functions (PDF)
1.2 The Cumulative Distribution Function (CDF)
1.3 Derivation under the Integral Sign (Leibniz's Rule)

Related concepts

Main connections

Compatible notation

Mathematical sample in LaTeX

The expression is rendered accessibly, with its LaTeX source preserved below.

P_X(B) = \mathbb{P}(X^{-1}(B)) = \int_{X^{-1}(B)} d\mathbb{P}(\omega) = \int_{B} dP_X(x)

View LaTeX source

P_X(B) = \mathbb{P}(X^{-1}(B)) = \int_{X^{-1}(B)} d\mathbb{P}(\omega) = \int_{B} dP_X(x)