RD Sharma Solutions for Class 12 Maths - Mean and Variance of a Random Variable - Free PDF Download
FAQs on RD Sharma Class 12 Maths Solutions Chapter 32 - Mean and Variance of a Random Variable
1. Why should a Class 12 student use RD Sharma solutions for the chapter on Mean and Variance of a Random Variable?
RD Sharma solutions offer a comprehensive set of well-graded problems for this chapter. They provide detailed, step-by-step explanations that go beyond basic NCERT exercises, helping students build a strong foundation and tackle complex questions. This is crucial for mastering the application of formulas for mean E(X) and variance Var(X).
2. How do the RD Sharma solutions for Chapter 32 help in preparing for the CBSE Class 12 board exams (2025-26)?
These solutions are aligned with the CBSE syllabus and help students master the expected problem types. By practising the variety of questions in RD Sharma, students can improve their speed and accuracy in calculating mean and variance. The solutions demonstrate the proper format for writing answers, which is essential for scoring full marks in board exams.
3. What is the step-by-step method shown in RD Sharma solutions to find the mean (or expected value) of a discrete random variable?
The solutions consistently follow a clear method:
- First, identify all possible values of the random variable X (let's say x₁, x₂, ..., xₙ).
- Next, calculate the probability P(X=xᵢ) for each value.
- Construct a probability distribution table with values of X and their corresponding probabilities P(X).
- Finally, calculate the mean or expected value, E(X), using the formula E(X) = ΣxᵢP(xᵢ).
4. How do you calculate the variance of a random variable using the formula Var(X) = E(X²) - [E(X)]², as explained in RD Sharma solutions?
The RD Sharma solutions break this down into a manageable process. After finding the mean E(X), you need to:
- Calculate E(X²) by using the formula E(X²) = Σxᵢ²P(xᵢ). This involves squaring each value of the random variable, multiplying by its probability, and summing the results.
- Square the mean that you calculated earlier to get [E(X)]².
- Substitute these two values into the variance formula: Var(X) = E(X²) - [E(X)]² to get the final answer.
5. What is a common mistake to avoid when calculating variance, and how do RD Sharma solutions help prevent it?
A very common mistake is confusing E(X²) (the mean of the squares of the random variable) with [E(X)]² (the square of the mean). The RD Sharma solutions clearly separate these two calculations. By showing the step-by-step process of first finding E(X), then finding E(X²), and only then subtracting, they help reinforce the correct operational order and prevent this conceptual error.
6. Why is creating a correct probability distribution table the most critical first step before finding mean and variance, as emphasized in RD Sharma solutions?
The entire calculation of mean and variance depends on the probability distribution table. If the probabilities are incorrect or do not sum to 1, every subsequent calculation, including E(X) and Var(X), will be wrong. RD Sharma solutions consistently start with building this table, highlighting its foundational importance for ensuring the accuracy of the final answer.
7. How do the solved examples in RD Sharma for this chapter clarify the practical difference between E(X²) and [E(X)]²?
The solved examples provide concrete numerical context. When you solve a problem, you might calculate a mean E(X) = 2.5, which makes [E(X)]² = 6.25. Then, you calculate E(X²) by summing the xᵢ²P(xᵢ) terms, which might result in a value like E(X²) = 7.5. By working through these distinct numerical calculations for the same problem, the abstract difference between the two terms becomes clear and tangible.
8. Are the problems in RD Sharma Chapter 32 sufficient for questions on this topic in competitive exams like JEE?
While RD Sharma provides an excellent foundation and is more extensive than NCERT, competitive exams like JEE Main often involve more complex applications. The solutions build the core skills needed, but students aiming for top ranks in JEE should supplement their practice with previous year's JEE papers and mock tests that focus on advanced problem-solving strategies for this topic.
