Gaussian distribution

What Gaussian distribution is

Gaussian distribution (also known as the normal distribution) is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean. It is a continuous probability distribution described by the normal curve, which is defined by its mean (μ) and standard deviation (σ).

Steps for Gaussian distribution:

  1. Calculate the mean (μ) and standard deviation (σ) of the data set.
  2. Plot the data on a graph, with the mean (μ) representing the center of the graph.
  3. Draw a bell-shaped curve on the graph, with the mean (μ) being the center and the standard deviation (σ) being the width.
  4. Determine the area under the bell-shaped curve. This area represents the probability of the data being within a certain range.
  5. Calculate the z-scores for each data point. Z-scores are the distance from the mean, expressed in standard deviation units.
  6. Calculate the probability of the data being within a certain range. This is done by calculating the area under the bell-shaped curve.

Examples

  1. Gauging the accuracy of predictions made by a linear regression model.
  2. Estimating the probability of an outcome based on a set of independent variables.
  3. Determining the probability of a certain value occurring within a data set.
  4. Estimating the probability of a stock’s return over a certain time frame.
  5. Estimating the probability of an event based on the average and standard deviation of related events.

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