Question: Show that each function defined as follows is a probability density function on the given interval; then find the indicated probabilities. (Round probabilities to 4

Show that each function defined as follows is a probability density function on the given interval; then find the indicated probabilities. (Round probabilities to 4 decimal places.) f(x) = 12 16 3x3 if 0 x 2 if x >

(a) P(0 ≤ X ≤ 2)

(b) P(X ≥ 2)
(c) P(1 ≤ X ≤ 3)

f(x) = 12 16 3x3 if 0 x 2 if x > 2

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