Random Variables Explained

Summary:

The note provides an overview of random variables, focusing on different types and their characteristics. It explains that a random variable is a variable that represents a random number and can assume various values based on the outcome of an experiment. Discrete random variables are discussed, which can take on a finite or countable number of values, often integers.

The concept of probability mass function is introduced, which calculates the probability of a random variable taking on specific values. The probability mass function is defined as a function that assigns probabilities to each value the random variable can take. The properties of the probability mass function, such as its sum being equal to one and the calculation of its standard deviation, are also mentioned.

The note concludes by mentioning that the probability mass function can be visualized using a bar chart, where the height of each bar represents the probability of the corresponding value of the random variable.

Overall, the note provides a concise explanation of random variables, their types, and the probability mass function, with examples to aid comprehension.

Excerpt:

Random Variables Explained

CHAPTER 2 Random Variable

A random variable is essentially a random number. Random variables are upper case letters and they can take on various values depending on the random outcome of an experiment. If the random variable is given by a capital letter, the corresponding small letter denotes the various values that the random variable can take on. Because the random variable depend on the random outcomes of the experiment given in ȳ, the random variable is a function of ȳ.

2.1 Discrete Random Variable

Discreet random variable: A random variable X is discreet if it can take on a finite (or infinite and countable) number of values, usually integers. Events are often expressed as random variables in statistic, and we have to calculate probabilities for these events (probability of the random variable).

Probability mass function: Suppose a random variable X can take on the values
ݔଵǡ ݔଶǡ ǥ(these values are known as mass points).