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Random Variables and Probability Distributions — Syllabus

Telangana Open School (TOSS) · Class 12 · Mathematics

What Random Variables and Probability Distributions covers in Telangana Open School (TOSS) Class 12 Mathematics: 4 topics, for the 2026-27 session.

49 questions25 flashcards9 formulas & key relations5 concepts

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4 Topics · Telangana Open School (TOSS) Class 12 Mathematics · 2026-27

Topics in Random Variables and Probability Distributions

1

Random Variables and Their Types

  • A random variable assigns numerical values to outcomes of a random experiment.
  • Discrete random variables take specific, countable values (e.g., number of heads in coin tosses).
  • Continuous random variables can take any value in an interval (e.g., time taken to complete a task).
2

Probability Distribution of a Discrete Random Variable

  • A probability distribution lists all possible values of a random variable and their corresponding probabilities.
  • Two conditions must be satisfied: (1) Each probability is ≥ 0, (2) Sum of all probabilities = 1.
  • This is often shown in a table format.
3

Mean, Variance, and Standard Deviation

  • Mean (expected value) is the long-run average value of repetitions of the experiment.
  • Variance measures how spread out the values are from the mean.
  • Standard deviation is the square root of variance and is in the same units as the variable.
4

Binomial Distribution

  • Used when there are fixed number of independent trials, each with two outcomes: success or failure.
  • Probability of success (p) remains constant across trials.
  • X ~ B(n, p) means X follows binomial distribution with parameters n and p.

Key Concepts

Central concept: Random Variables and Probability Distributions

Random VariableDiscrete Random VariableProbability DistributionMean, Variance, Standard DeviationBinomial DistributionPoisson Distribution

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Frequently Asked Questions

What are the important topics in Random Variables and Probability Distributions for Telangana Open School (TOSS) Class 12 Mathematics?
Key topics in Random Variables and Probability Distributions include Random Variables and Their Types, Probability Distribution of a Discrete Random Variable, Mean, Variance, and Standard Deviation, Binomial Distribution. Study these first, then practise questions on each for the Telangana Open School (TOSS) Class 12 board exam.
How should I revise Random Variables and Probability Distributions for the Telangana Open School (TOSS) Class 12 board exam?
Learn the core ideas first, then work through the 49 practice questions on Random Variables and Probability Distributions. Revise definitions regularly and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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All Telangana Open School (TOSS) Class 12 Mathematics Syllabus

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