A theoretical distribution represents all possible outcomes and their associated probabilities for a random variable under certain assumptions. It provides information about how likely different values are to occur.
Imagine you are playing a board game with dice. The theoretical distribution would be a chart showing the probabilities of rolling each number on the dice, helping you understand which numbers are more likely to come up.
Empirical Distribution: An empirical distribution is based on observed data and represents the frequencies or proportions of different values in a sample.
Normal Distribution: A normal distribution is a bell-shaped theoretical distribution that occurs naturally in many real-world phenomena, characterized by its mean and standard deviation.
Binomial Distribution: A binomial distribution is a theoretical distribution that models the number of successes in a fixed number of independent Bernoulli trials, where each trial has two possible outcomes (success or failure).
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