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Variance of Random Variable - Probability, Class 12, Math Video Lecture | Mathematics (Maths) Class 12 - JEE

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FAQs on Variance of Random Variable - Probability, Class 12, Math Video Lecture - Mathematics (Maths) Class 12 - JEE

1. What is variance of a random variable?
Ans. Variance of a random variable is a measure of how much the values of the variable vary around the expected value. It provides information about the spread or dispersion of the probability distribution of the random variable.
2. How is variance calculated for a random variable?
Ans. The variance of a random variable can be calculated by taking the average of the squared differences between each value of the random variable and its expected value. Mathematically, it can be expressed as Var(X) = E((X - E(X))^2), where E(X) represents the expected value of the random variable.
3. What does a high variance indicate for a random variable?
Ans. A high variance for a random variable indicates that the values of the variable are spread out over a larger range and are more dispersed. It suggests that there is a greater degree of uncertainty or variability in the possible outcomes of the random variable.
4. How does variance relate to the probability distribution of a random variable?
Ans. Variance is a measure of the spread or dispersion of the probability distribution of a random variable. It quantifies how much the values of the random variable deviate from the expected value. A higher variance indicates a wider distribution, while a lower variance indicates a narrower distribution.
5. Can variance be negative for a random variable?
Ans. No, variance cannot be negative for a random variable. Variance is defined as the average of the squared differences between each value of the random variable and its expected value. Since squared differences are always non-negative, the variance will always be non-negative as well.
204 videos|288 docs|139 tests

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