Lesson Plan

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Lesson Plan
Grade: Date: 03/03/2026
Subject: Mathematics
Lesson Topic: Discrete random variables: probability distributions, expectation, variance
Learning Objective/s:
  • Define a discrete random variable and its probability mass function (PMF).
  • Construct and interpret the cumulative distribution function (CDF) for a discrete variable.
  • Calculate expectation and variance using summation formulas and apply linearity properties.
  • Identify and apply formulas for common discrete distributions (binomial, Poisson, geometric).
  • Solve a worked example involving the sum of two dice to find its PMF, mean, and variance.
Materials Needed:
  • Projector or interactive whiteboard
  • Slide deck with definitions and formulas
  • Handout containing the dice‑sum table
  • Graph paper or digital graphing tool for PMF bar charts
  • Calculator or computer algebra system
  • Worksheets for practice problems
 Introduction:
Begin with a quick question: “If you roll two dice, what outcomes are possible for the sum?” Connect this to prior work on single‑event probabilities and highlight the need for a systematic way to describe outcomes of discrete variables. State today’s success criteria: define discrete random variables, construct their PMFs and CDFs, and compute expectation and variance.
Lesson Structure:
  1. Do‑Now (5'): Students list possible sums of two dice on sticky notes; teacher checks understanding of the sample space.
  2. Direct Instruction (10'): Present definitions of discrete RV, PMF, and CDF with examples on the screen.
  3. Guided Practice (12'): Construct the PMF table for the dice sum together and calculate the CDF cumulatively.
  4. Conceptual Focus (8'): Derive expectation and variance formulas; demonstrate the linearity property with simple examples.
  5. Worked Example (15'): Walk through the provided dice example, computing mean and variance step‑by‑step while students follow on worksheets.
  6. Independent Practice (10'): Students solve a short problem on the binomial distribution, computing its mean and variance; teacher circulates to support.
  7. Summary & Check (5'): Quick exit‑ticket quiz with three questions – define PMF, compute E(X) for a given distribution, and state the variance formula.
Conclusion:
Review the key steps: defining a discrete variable, building its PMF and CDF, and using summation formulas for expectation and variance. For the exit ticket, students write one example of a discrete distribution and its mean. Homework: complete a worksheet on binomial and Poisson distributions, including calculations of probabilities, means, and variances.