Currently Empty: $0.00
5.Probability Distributions
Class 12 • Mathematics • NCERT
Random Variables
[ Embed Your Video Lecture Here ]
This lesson introduces random variables, which assign numerical values to outcomes of a random experiment, as prescribed in NCERT Class 12 Probability.
Lesson Objectives
- Understand the meaning of a random variable.
- Distinguish between discrete and continuous random variables.
- Represent random variables mathematically.
- Prepare for NCERT board-level questions.
1. Meaning of Random Variable
A random variable is a real-valued function that assigns a numerical value to each outcome of a random experiment.
Random variables are usually denoted by capital letters like X, Y.
[ Image Placeholder: Mapping of Sample Space to Numbers ]
2. Definition (NCERT)
Let S be the sample space of a random experiment. A random variable X is a function from S to the set of real numbers.
X : S → R
[ Image Placeholder: Function Representation of Random Variable ]
3. Discrete Random Variable
A random variable is called discrete if it takes a finite or countably infinite number of values.
Example: Number of heads when tossing two coins.
[ Image Placeholder: Discrete Outcomes ]
4. Continuous Random Variable
A random variable is called continuous if it can take any value within a given interval.
Example: Height of students in a class.
[ Image Placeholder: Continuous Values on Number Line ]
5. NCERT Example
A coin is tossed two times.
Let X be the number of heads obtained.
Then X can take values 0, 1, 2.
Let X be the number of heads obtained.
Then X can take values 0, 1, 2.
[ Image Placeholder: Coin Toss Outcomes ]
6. Important NCERT Notes
• Random variable assigns numbers to outcomes
• Discrete variables have countable values
• Continuous variables take interval values
• Foundation for probability distribution
• Discrete variables have countable values
• Continuous variables take interval values
• Foundation for probability distribution
Practice Questions (NCERT)
- Define a random variable.
- What is meant by a discrete random variable?
- What is a continuous random variable?
- Give one example of a discrete random variable.
- Give one example of a continuous random variable.
- What does X : S → R represent?
- Can a random variable take negative values?
- Is random variable part of NCERT Class 12 syllabus?
- Is this concept important for board exams?
- Which topic follows random variables in NCERT?
✅ Show Answer Key
- Function assigning numbers to outcomes
- Takes finite or countable values
- Takes values in an interval
- Number of heads
- Height of a person
- Function from sample space to real numbers
- Yes
- Yes
- Yes
- Probability Distribution
© Aviate Learning – Random Variables (NCERT Class 12)