The study of uncertainty through assigning probabilities to events. Random variables represent outcomes in probability experiments, while probability distributions describe their possible values and associated probabilities.
Probability, random variables, and probability distributions are like predicting the outcome of rolling a fair six-sided die. The probability of rolling any specific number is 1/6 (probability), the numbers on the die represent possible outcomes (random variables), and the distribution shows how likely each outcome is (probability distribution).
Discrete Random Variable: A random variable that can only take on a countable number of values, such as the number of heads in multiple coin flips.
Continuous Random Variable: A random variable that can take on any value within a certain range, such as the height of students in a class.
Normal Distribution: A symmetric probability distribution that follows a bell-shaped curve, commonly used to model many natural phenomena.
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