What is a probability distribution

Answer

A probability distribution is a mathematical function or model that describes the likelihood of different outcomes or events in a random experiment. It shows how probabilities are assigned to different values of a random variable, either discrete or continuous.

Types of Probability Distributions

1. Discrete Probability Distribution: Used for random variables that take a finite or countable number of distinct values (e.g., number of heads in coin tosses).

2. Continuous Probability Distribution: Used for random variables that take an infinite number of values within a range (e.g., height, weight, or time).

Key Elements of a Probability Distribution

1. Random Variable: A variable that can take on different values based on the outcome of a random event or process. It can be:

   • Discrete: Takes specific, separate values (e.g., the number of cars sold).

   • Continuous: Takes any value within a range (e.g., the time it takes for a computer to process data).

2. Probability Function (PMF or PDF):

           PMF (Probability Mass Function): For discrete random variables, it assigns probabilities to each possible value.

   
   

   • PDF (Probability Density Function): For continuous random variables, it defines the likelihood of a random variable lying in a given range of values. The probability is given by the area under the curve for a range of values.

3. Cumulative Distribution Function (CDF): The CDF gives the probability that the random variable is less than or equal to a certain value. It sums the probabilities (discrete) or integrates the density (continuous) up to that point.

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