### Continuous Random Variable Probability Density FunctionLet \( X \) be a continuous random variable whose probability density function is given by the formula:\[ p(x) = \begin{cases} \frac{1}{27}x & \text{if } 0 \leq x \leq 6 \\[8pt]\frac{2}{3} - \frac{2}{27}x & \text{if } 6 \leq x \leq 9 \\[8pt]0 & \text{otherwise}\end{cases} \]Find the probability that \( X \) is between 3 and 9. Enter the exact answer as a fraction (not a decimal approximation).

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Answered: Let X be a continuous random variable…

A First Course in Probability (10th Edition)

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Let X be a continuous random variable whose probability density function is given by the formula if 0 ≤ x ≤ 6 xif 6 ≤x≤9 otherwise. p(x) = 27x 22/000 0 - Find the probability that X is between 3 and 9. Enter the exact answer as a fraction (not a decimal approximation).