Question: 3. Suppose a continuous random variable X has the Probability Density Function 0 $330; as: 0 2, where a > 0 is a constant. (a)

3. Suppose a continuous random variable X has the Probability Density Function 0 $330; as: 02, where a > 0 is a constant. (a) (1 point) Determine P(1 g X 5 2). (b) (1 point) Determine P(1 S X 5 5). (c) (2 points) By considering If; f (:12) d3: or otherwise, determine a. ) (d (4 points) Write down the Cumulative Distribution Function of X. (The answer will be piecewise-dened.)

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