If the difference between the expectation of the square of a random variable ( E [X])2 is denoted by R, thena)R = 0b)R 0Correct answer is option 'C'. Can you explain this answer?

Question

If the difference between the expectation of the square of a random variable ( E [X])2 is denoted by R, thena)R = 0b)R< 0c)R &ge; 0d)R > 0Correct answer is option 'C'. Can you explain this answer?

Answer

= 0 implies that the variable X has no variance or variability. In other words, it means that X always takes on the same value, so there is no difference between the expected value of X squared and the square of the expected value of X. This is a special case and not true for most random variables.

b) R > 0 implies that the variable X has some variance or variability. In this case, there is a difference between the expected value of X squared and the square of the expected value of X. This is the more typical scenario for random variables.

Answer

We know,
The second control momnt,
μ₂ = E{X-m)}² [m = mean of the distribution of X]
= E(X²)−2m×E(X) + m²
= E(X²)−2[E(X)]² + E(X) [∴ m = E(X)]
E (X²) − [E ( X)]²

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