A quantity X has cumulative distribution function P(x) = 0.75x - x^2/8 for 0 ? x ? 4 and P(x) = 0 for x < 0 and P(x) = 1 for x > 4 . Find the mean and median of X . Enter the exact answers. Mean = 2/3 Median = 0.764
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Since P(x) = 0.75x for 0 ≤ x ≤ 4, we have: f(x) = \frac{dP(x)}{dx} = \frac{d(0.75x)}{dx} = 0.75 Now, we can find the mean and median of X. Mean (µ) is given by the formula: µ = \int_{-\infty}^{\infty} xf(x)dx Since f(x) = 0.75 for 0 ≤ x ≤ 4 and f(x) = 0 Show more…
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