Tuitions

Expert tutoring,
exam-ready results.

Structured live sessions for students. Small groups, real mentors, exam-focused content.

Back to Probability & Statistics
Intermediate 8 Hours Article 23.16

Joint Probability Distributions

Joint PMF, marginal distributions, covariance, and independence

✓ Live group sessions (full course duration) ✓ Dedicated doubt-clearing within the batch

Pricing (per student)

10+ students
₹150 / hr
Total: ₹1,200
15+ students
₹125 / hr
Total: ₹1,000
20+ students
₹100 / hr
Total: ₹800

Prerequisites

  • Completion of Probability Distributions — Discrete and Continuous (or equivalent)

Overview

Introduces joint probability distributions for two discrete random variables. Students calculate marginal and conditional distributions, expectation, covariance, and test for independence — all aligned to exam problem patterns.

Topics

HourTopicDetails
1Joint Probability Mass FunctionDefinition, properties, and worked examples.
2Marginal & Conditional DistributionsCalculation and interpretation.
3Expectation for Joint DistributionsMean and variance calculations.
4Covariance & CorrelationDefinition, calculation, and interpretation.
5Problem-Solving (Article 23.16)Solving joint probability problems from the textbook.
6Independence of Random VariablesDefinition, conditions, and counter-examples.
7Additional Problem-SolvingMixed joint probability problems.
8Recap & Doubt ClearingRevision and timed Q&A session.

Expected Outcomes

  • Understand joint, marginal, and conditional distributions.
  • Calculate expectation, covariance, and correlation for joint distributions.
  • Test for independence between two random variables.