2/26/2021

Questions on Binomial Random Variables (we will return to this topic in Chapter 4)

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.

Properties of means and variances

Class Activity - Means and Variances of Discrete Random Variables

Bayes' Theorem

Class Activity - Applications of Bayes' Theorem

We will begin Chapter 4 on Monday so please read Section 4.1 for class on Monday.