Let X be a continuous random variable whose probability density function is given by the formula if 0≤x≤5 20 -{t x if 5 ≤ x ≤ 8 otherwise. p(x) = Find the probability that X is between 3 and 7. Enter the exact answer as a fraction (not a decimal approximation).
Let X be a continuous random variable whose probability density function is given by the formula if 0≤x≤5 20 -{t x if 5 ≤ x ≤ 8 otherwise. p(x) = Find the probability that X is between 3 and 7. Enter the exact answer as a fraction (not a decimal approximation).
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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![**Problem:**
Let \( X \) be a continuous random variable whose probability density function is given by the formula:
\[ p(x) = \begin{cases}
\frac{1}{20} x & \text{if } 0 \le x \le 5 \\
\frac{2}{3} - \frac{1}{12} x & \text{if } 5 \le x \le 8 \\
0 & \text{otherwise.}
\end{cases} \]
Find the probability that \( X \) is between 3 and 7. Enter the exact answer as a fraction (not a decimal approximation).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F85a13651-0641-4e1f-9366-64e873b85445%2Fc5dfc323-372d-4534-9533-5eb772673c4b%2Fap9ok1l_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem:**
Let \( X \) be a continuous random variable whose probability density function is given by the formula:
\[ p(x) = \begin{cases}
\frac{1}{20} x & \text{if } 0 \le x \le 5 \\
\frac{2}{3} - \frac{1}{12} x & \text{if } 5 \le x \le 8 \\
0 & \text{otherwise.}
\end{cases} \]
Find the probability that \( X \) is between 3 and 7. Enter the exact answer as a fraction (not a decimal approximation).
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