Given the probability density function f(x) = 1/2 over the interval [1, 3], find the expected value, the mean, the variance and the standard deviation. Expected value: Mean: Variance: Standard Deviation:
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\[ E(X) = \int_{1}^{3} z \cdot f(z) \, dz = \int_{1}^{3} z \cdot \frac{1}{2} \, dz = \frac{1}{2} \int_{1}^{3} z \, dz = \frac{1}{2} \left[ \frac{z^2}{2} \right]_{1}^{3} = \frac{1}{2} \left( \frac{9}{2} - \frac{1}{2} \right) = \frac{4}{2} = 2 \] ** Show more…
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