Discrete

1. Bernoulli Distribution

   • What: Models a single event with two possibilities (success or failure).
   • Example: Tossing a coin (heads or tails), checking if a website visitor made a purchase (yes or no).

2. Binomial Distribution

   • What: Counts the number of successes in a fixed number of repeated Bernoulli trials (with the same probability of success each time).
   • Examples:
     • Flipping a coin 10 times, the distribution models the probability of getting various numbers of heads.
     • Number of defective products in a batch if each product has a known defect probability.

3. Poisson Distribution

   • What: Models the number of events occurring in a fixed interval (time or space) with a known average rate.
   • Examples:
     • Number of customers arriving at a store per hour.
     • Number of website errors in a day.
     • Number of earthquakes of a certain magnitude in a region within a year.

4. Geometric Distribution

   • What: Models the number of trials needed to get the first success in repeated Bernoulli trials.
   • Examples:
     • Number of coin flips needed to get the first head.
     • Number of attempts to start a faulty engine before it finally turns on.

5. Negative Binomial Distribution

   • What: Generalization of the geometric distribution. This models the number of trials needed to achieve a fixed number of successes.
   • Example: Number of lottery tickets bought before hitting the jackpot three times.

   Continuous

   1. Normal Distribution (Gaussian Distribution)
      • What: The ubiquitous bell-shaped curve. Symmetrical, characterized by mean (center) and standard deviation (spread).
      • Examples:
        • Heights of adult humans in a population.
        • Measurement errors in a scientific experiment.
        • Stock price fluctuations over short periods.
   2. Uniform Distribution
      • What: Describes an equal probability for all values within a specified range.
      • Examples:
        • Outcome of rolling a fair dice (equal chance for 1, 2, 3, ... , 6).
        • Randomly generating numbers within a certain interval.
   3. Exponential Distribution
      • What: Models the time between events occurring at a constant average rate (often used in Poisson processes).
      • Examples:
        • Time until a radioactive particle decays.
        • Time between customer arrivals at a bank.
        • Lifetime of a lightbulb.
   4. Chi-Squared Distribution
      • What: A distribution formed from the sum of squared standard normal variables. Important for hypothesis testing and confidence intervals.
      • Example:
        • Analyzing the variance of sample data.
   5. Student's t-Distribution
      • What: Similar to the normal distribution but with heavier tails. Used for inference about population means when the sample size is small or population standard deviation is unknown.
      • Example:
        • Estimating the average salary of a company with data from a small sample of employees.