1 Random Variable and Probability Distributions

• Statistics is a branch of mathematics which is used to summarize, interpret, and analyze the things we observe and to bring meaning in this life.
• Inferential statistics which makes inferences about populations using data drawn from the population.
• Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur. It also tells us how often some event will happen after many repeated trials.
• An experiment is any procedure that can be infinitely repeated and has a well-defined set of possible outcomes.
• A random experiment which refers to a procedure that generates well-defined outcomes but the outcomes cannot be predicted.
• The set of all possible outcomes in an experiment is called the sample space, denoted by S. The elements in the sample space are called sample points.
• A random variable is a variable whose possible values are determined by chance and is dependent to the outcome of the random experiment. The term “random” is used to emphasize that the outcome cannot be determined with certainty.
• A random variable is usually denoted by capital letters, oftentimes X or Y. It is a function that assigns a unique real number to each element in the sample space.
• Discrete Random Variable can only take a finite (countable) number of distinct values. Distinct values mean values that are exact and can be represented by nonnegative whole numbers.
• Continuous Random Variable can assume an infinite number of values in an interval between two specific values. These means they can assume values that can be represented not only by nonnegative whole numbers but also by fractions and decimals.
• The possible values of a random variable are values that are obtained from functions that assign a real number to each point of a sample space.