Let f(x) = kx2(5 − x) if 0 ≤ x ≤ 5 and f(x) = 0 if x < 0 or x > 5. (a) For what value of k is f a probability density function? k = (b) For that value of k, find P X ≥ 52 . (c) For that value of k, find the mean.
Added by Chase A.
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The function is defined as: \[ f(x) = kx^2(5 - x) \quad \text{for } 0 \leq x \leq 5 \] We need to compute the integral: \[ \int_0^5 f(x) \, dx = \int_0^5 kx^2(5 - x) \, dx \] Show more…
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