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Let x1, x2,..., x10 be ten observations of a random variable X. If sum of (xi - lambda) = 3 and sum of (xi - lambda)² = 13, then the variance of these observations is:

1. 1.35
2. 1.31
3. 1.21
4. 1.25

Correct answer: 1.21

Solution

Shifting all observations by a constant (lambda) does not change the variance. With yi = xi - lambda: Var(X) = Var(Y) = (1/10)*sum(yi²) - [(1/10)*sum(yi)]² = 13/10 - (3/10)² = 1.3 - 0.09 = 1.21.

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