Mr. S Teaches
Sign inRequest Tutoring
Menu
Sign inRequest Tutoring

Statistics and Probability · 35 minutes

Suggested grades 10–12 · Unit 3: Independence and expected value · Lesson 2 of 2

Expected Value for Resource Demand

Interpret a weighted probability mean without treating it as a guaranteed daily count.

Mr. S Teaches · Original starter lesson · HS-STAT-06 · Grade range is planning guidance.

Watch, notice, discuss

Video choices for this lesson

2 choices

Preview a video, then choose what fits your learners. “Show to class” opens a larger view; use the player’s play and full-screen controls when you’re ready.

Teacher preview needed. Check the language, level and length before showing. YouTube may show ads or related videos.

OPTION 2 · YOUTUBE

Constructing a probability distribution for random variable | Khan Academy

By Khan Academy

Check that outcomes and probabilities form a valid distribution before calculating expected resource demand.

Open on YouTube: Constructing a probability distribution for random variable | Khan Academy (opens a new tab) ↗
After watching

Why can an expected demand be useful even when that exact demand cannot happen on a single day?

An external player loads only after you choose Preview or Show to class. Playback connects to YouTube. Videos belong to their creators; availability and embedding can change.

Learning objective

Calculate an expected value and explain its long-run meaning and planning limitation.

Before you begin

  • Probability distributions
  • Weighted arithmetic

Gather your materials

  • Paper and pencil
  • Graph paper
  • Calculator for checking results

Language to know

random variable
A numerical quantity assigned to outcomes of a chance process.
probability distribution
Possible variable values with their assigned probabilities.
expected value
The probability-weighted mean of the variable’s values.

Understand the concept

A fictional library predicts daily requests for a repair manual:0 requests with probability 0.2,1 with 0.5 and 2 with 0.3. The expected number is a weighted mean, not the most likely count and not necessarily a possible single-day outcome. Planning also depends on variation and consequences of shortages; expectation alone is not a guarantee.

Teach it step by step

  1. Check that probabilities are nonnegative and sum to 1 before calculating.
  2. Multiply each demand by its probability and add the contributions.
  3. Compare expected value with the most likely outcome and the possible daily values.
  4. Use the model to estimate a30-day total while noting that an actual month may differ.

Make the thinking visible

Worked example or model response

E(X)=0(0.2)+1(0.5)+2(0.3)=1.1 requests/day. The most likely count is 1. Over 30 modeled days, the expected total is 33 requests; no single day must have 1.1 requests.

Guided practice

Calculate expected demand for values 0,1,3 with probabilities 0.25,0.5,0.25.

Independent practice

1. Find expected value for 2,4,6 with probabilities 0.2,0.3,0.5. 2. Explain why an expectation of 4.6 does not identify the most likely outcome. 3. Identify an invalid distribution with probabilities 0.4,0.4,0.4.

Quick assessment

Can an expected value lie between possible outcomes without itself being possible?

Answer key & assessment criteria

Answers and teaching guidance

  1. Guided: E=0+0.5+0.75=1.25.
  2. Independent 1:0.4+1.2+3=4.6. 2: The most likely value here is 6, with probability 0.5; the mean uses all outcomes. 3: The probabilities sum to 1.2, so they are invalid.
  3. Quick check: Yes. A weighted mean need not equal any individual outcome.

Look for: Require the learner to explain the interpretation and check, not only state a result. Distinguish an exact value from a rounded approximation and attend to the stated domain.

Make it work for your learner

More support

Use a probability×value table with separate contribution and total columns.

Extension challenge

Construct two demand distributions with equal expected values but different shortage risks for a one-item supply.

Verified references · Selected contributions

Standards connections

Subject-content standards

These records identify the part of a subject standard practiced here. Course placement is instructional guidance; the source’s category or band remains authoritative.

Contributes to Common Core standard

HSS.MD.A.2

Common Core · High school · Statistics and Probability

(+) Additional preparation for advanced study

Calculate a random variable’s expected value and interpret the distribution’s mean.

Read the official standard ↗

Additional preparation (+). The supplied discrete model introduces expected value; constructing and validating a model and decision criteria require further study.

Verified 2026-11-04. Selected contribution, not full attainment.