Probability Distribution

• Probability distribution of a discrete random variable/Probability distribution function/Probability mass function

  • a list, a table, a graph, a formula of possibilities associated with each of its possible values

  Properties:

  1. 0≤ P(X=Xᵢ) ≤ 1
  2. Σ P(X=Xᵢ) = 1
• Discrete Probability Distribution

  • a list of possibilities for each of the possible outcomes
  • values of random variable and corresponding probabilities
• Normal Distribution

  • most of the scores tend to be closer to the mean
  • continuous probability distribution
  • random variable is normal random variable (continuous random variable)
• Standard Normal Distribution

  • example of a normal distribution
  • mean of 0 and standard deviation of 1
• mean (μ "mu) - center of normal curve
• standard deviation (σ "sigma") - the spreadness of distribution
• Characteristics of a Normal Random Variable:

  1. A normal distribution is symmetric about its mean.
  2. The mean, median, mode of a normal distribution are all equal and located at center
  3. A normal distribution is thicker at the center and less thick at the tails
  4. Approximately 68.26% of the area of normal distribution is within one standard deviation of the mean
  5. Approx. 95.44% within two standard deviation of the mean
  6. Approx. 99.74% within three standard deviation of the mean
• Outliers - scores that are more than two standard deviation away from the mean
• Extreme Outliers - scores that are more than three standard deviation away from the mean