RD Sharma Class 12 Solutions Chapter 32 - Mean and Variance of a Random Variable (Ex 32.2) Exercise 32.2

Q: 4. Why is the formula Var(X) = E(X²) - [E(X)]² used more frequently in these solutions than the basic definition E[(X - μ)²]?

The formula Var(X) = E(X²) - [E(X)]² is computationally more efficient and less prone to errors, especially when the mean (μ or E(X)) is a fraction or a decimal. Calculating (X - μ)² for each value can be tedious. The preferred formula simplifies the process into two clear steps: finding the mean of X and finding the mean of X², which makes it a more reliable method for exam purposes, as demonstrated in the solutions for Exercise 32.2.

Q: 5. What does it mean conceptually if the variance of a random variable is zero?

If the variance of a random variable is zero, it implies that there is no variability or spread in the data. This means the random variable is not random at all; it is a constant. All of its probability is concentrated at a single value, which is its mean. For example, if Var(X) = 0, then the random variable X will only take one value with a probability of 1.

RD Sharma Class 12 Solutions Chapter 32 - Mean and Variance of a Random Variable (Ex 32.2) Exercise 32.2 - Free PDF

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RD Sharma Class 12 Solutions Chapter 32 - Mean and Variance of a Random Variable

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FAQs on RD Sharma Class 12 Solutions Chapter 32 - Mean and Variance of a Random Variable (Ex 32.2) Exercise 32.2

1. Where can I find accurate, step-by-step solutions for every question in RD Sharma Class 12 Maths, Exercise 32.2?

You can find clear, step-by-step solutions for all problems in RD Sharma Class 12 Maths Exercise 32.2 right here on this page. Each solution is prepared by subject matter experts to ensure correctness and adherence to the CBSE-prescribed methodology for finding the mean and variance of a random variable.

2. What is the correct formula to calculate the variance of a random variable (Var(X)) as used in the solutions for Chapter 32?

The solutions for this chapter primarily use the standard formula for variance, which is highly efficient for calculations. The formula is:

Var(X) = E(X²) - [E(X)]²

Where:

E(X) is the mean or expected value of the random variable X.
E(X²) is the expected value of X².

This method is broken down in the solutions to make it easy to follow.

3. How do the RD Sharma solutions for Ex 32.2 help in avoiding common calculation mistakes?

These solutions help prevent common errors by providing a structured and methodical approach. Key steps like creating a probability distribution table, calculating pᵢxᵢ for the mean, and then calculating pᵢxᵢ² for the variance are shown distinctly. This systematic breakdown minimises the chances of arithmetic mistakes and helps you understand the process, not just the final answer.

4. Why is the formula Var(X) = E(X²) - [E(X)]² used more frequently in these solutions than the basic definition E[(X - μ)²]?

The formula Var(X) = E(X²) - [E(X)]² is computationally more efficient and less prone to errors, especially when the mean (μ or E(X)) is a fraction or a decimal. Calculating (X - μ)² for each value can be tedious. The preferred formula simplifies the process into two clear steps: finding the mean of X and finding the mean of X², which makes it a more reliable method for exam purposes, as demonstrated in the solutions for Exercise 32.2.

5. What does it mean conceptually if the variance of a random variable is zero?

If the variance of a random variable is zero, it implies that there is no variability or spread in the data. This means the random variable is not random at all; it is a constant. All of its probability is concentrated at a single value, which is its mean. For example, if Var(X) = 0, then the random variable X will only take one value with a probability of 1.

6. Are the solutions for RD Sharma's chapter on Mean and Variance aligned with the latest CBSE Class 12 Maths syllabus (2025-26)?

Yes, the solutions provided for RD Sharma Class 12 Chapter 32 are fully aligned with the topics of Mean and Variance of a Random Variable as prescribed in the latest CBSE syllabus for the 2025-26 academic year. The methods and formulas used are exactly what is expected in board examinations.