Mathematics · Probability and Statistics
Let p(x) be the probability density function for a positive real variable x, and g(α) = ∫0∞ p(x) e-αx dx. If g'(α) and g''(α) are the first and second derivatives of g(α) with respect to α, which of the following gives the variance of x?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1g''(0)g'(0)g(0)
- 2[g''(0) - g'(0)]2
- 3g''(0) + [g'(0)]2
- 4g''(0) - [g'(0)]2✓
Correct answer
g''(0) - [g'(0)]2
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