**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).

To find the probability that X is between 3 and 7, we need to calculate the definite integral of the…

Answered: Let X be a continuous random variable…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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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).