016 - Normalize Distribution Solution

Understanding Division and Probability Distribution

Basic Division Illustrations

• 0.12 divided by 0.36

  • Simplifies to 12 divided by 36, which equals 1/3.

  • Numerically approximated as 0.333.

• 0.04 divided by 36

  • Simplifies to 4 divided by 36, which equals 1/9.

Additive Combinations

• When examining the fractions:

  • 0.333 (one-third) + 0.333 (one-third) + 0.111 (three-ninths) gives exactly 1.

  • This demonstrates a form of probability distribution.

Probability Distribution Explanation

• A probability distribution assigns probabilities to different outcomes.

• Written as:

  • P(I), where I can range from 1 to 5 based on measurements observed.

  • The probabilities reflect the likelihood of each outcome given evidence from the measurement z.

Posterior Distribution

• The distribution discussed is also termed the posterior distribution:

  • P(x_i | z): This reads as probability of x_i given measurement z.

  • It represents updated beliefs about the probabilities after new information is factored in (measurement z).

Implementation

• To apply these concepts:

  • Recognize how initial fractional simplifications relate to probability in practical scenarios.

  • Use the structure of the probability function to evaluate outcomes with given measurements.