(50 points) Consider a continuous random variable with the following pdf: $f(x) = \begin{cases} \frac{1}{2} & 0 \le x \le 1\\ \frac{3-x}{4} & 1 \le x \le 3 \end{cases}$ Develop a random-variate generator for the random variable X by using the inverse-transform technique.
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The CDF is defined as the integral of the probability density function (PDF) from negative infinity to x. In this case, the PDF is given as: f(x) = 0, for x < a f(x) = 1, for a ≤ x ≤ 1 To find the CDF, we integrate the PDF: F(x) = ∫[a,x] f(t) dt For x < a, the Show more…
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