2.2 Estimators

Exercise 1: Understanding Estimators Let’s start with the basics! Given sample data, write down the formulas for:

  1. The best estimator of a random variable’s expectation.
  2. The best estimator of a random variable’s variance.

Answers:

  • Estimator for a RV’s expectation: ___
  • Estimator for a RV’s variance: ___


Exercise 2: Estimating Expected Value A real estate analyst collected data on the percentage change in home values over one year for six properties:

{5.2%, -1.8%, 7.5%, 4.9%, 6.1%, 3.2%}

Your task: What is the best estimate for the expected value of the random variable “annual percentage change in home value”? Use R code to solve this problem.

Answer:

homes <- c(_____, _____, _____, _____, _____, _____)  
avg <- sum(_____) / length(_____)  
avg


Exercise 3: Estimating Variance Using the same data from Exercise 2, what is the best estimate for the variance of the random variable “annual percentage change in home value”? Use R code to solve this problem.

Answer:

sum((_____ - _____)^2) / (length(_____) - 1)


Exercise 4: Checking Your Work Let’s verify your answers to Exercises 2 and 3 using R’s built-in functions:

  • mean() estimates the expected value of a RV.
  • var() estimates the variance of a RV.

Answer:

mean(_____)  
var(_____)