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Let x_i (1 ≤ i ≤ 10) be observations of a random variable X. If ∑ from i=1 to 10 (x_i - p) = 3 and ∑ from i=1 to 10 (x_i - p)² = 9 where 0 ≠ p ∈ R, then the standard deviation of these observations is.

1. √(3/5)
2. 9/10
3. 4/5
4. 7/10

Correct answer: 9/10

Solution

The standard deviation is calculated using the formula for variance, which is the average of the squared deviations from the mean. Given that the sum of squared deviations is 9 and there are 10 observations, the variance is 9/10, leading to a standard deviation of √(9/10) = 3/√10, which simplifies to 9/10.

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