2/13/2023

Discussion of Quiz #2.

The mean (expected value) and standard deviation of a random variable

• Mean (or Expected Value) of X
  • If X is a discrete random variable taking values x₁, x₂, …, x_k with probabilities p₁, p₂, …, p_k the mean (or expected value) of X is given by µ=E[X] = x₁*p₁ + x₂*p₂ + ... + x_k*p_k.
• Variance of X
• If X is a discrete random variable taking values x₁, x₂, …, x_k with probabilities p₁, p₂, …, p_k the variance of X is given by Var[X] = (x₁-µ)²*p₁ + (x₂-µ)²*p₂ + (x_k-µ)²*p_k.
• The standard deviation of X is the square root of the variance.

Conditional Probability and Bayes Theorem - (see Section3.2_Conditional_Probability_Bayes_Rule.pdf in our !Class-Notes Google Drive folder.

Properties of means and variances - (see Section3.4_Means_Variances.pdf)

Class Activities - See handouts

• Applications of Bayes Theorem
• Means and Variances of Discrete Random Variables

Please complete your reading of Section 4.1 for class on Wednesday.