Last updated: 2019-04-25

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Knit directory: MSTPsummerstatistics/

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Rmd 68d1b40 Anthony Hung 2019-04-24 Start probability intro
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Introduction

Probability is a foundational concept in statistics, and understanding the basics of probability is important for understanding the theory behind commonly used statistical tests and developing statistical methods. Here, we discuss the basics behind random variables and their probability distributions.

Random Variables

Random variables are variables that can take on a set of possible numerical values, each of which has a probability of occuring. Oftentimes the numerical values that a random variable takes on represents a particular outcome. For example, the result of a coin flip can be thought of as a random variable that can take on one of two values: heads or tails, each with a probability \(\frac{1}{2}\) of occuring.

X(x)

Value Outcome Probability
\(0\) \(heads\) \(P_{heads} = \frac{1}{2}\)
\(1\) \(tails\) \(P_{tails} = \frac{1}{2}\)

Properties of Random Variables

Types of distributions: Discrete vs. Continuous

Working with named distributions in R