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If E denotes expectation, the variance of a random variable X is given by

1. E[X²] - E²[X]
2. E[X²] + E²[X]
3. E[X²]
4. E²[X]

Correct answer: E[X²] - E²[X]

Solution

The variance of a random variable is defined as the expected value of the squared deviation from the mean, which mathematically is expressed as E[X²] minus the square of the expected value E[X]. This captures the spread of the random variable around its mean.

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