What is the probability that total waiting time is at most 4 min?What is the probability that total waiting time is between 4 and 8 min?What is the probability that total waiting time is either less than 3 min or more than 9 min? In commuting to work, a professor must first get on a bus near her house and then transfer to a second bus. If the waiting time (in minutes) at each stop has a uniform distribution with \( A = 0 \) and \( B = 5 \), then it can be shown that the total waiting time \( Y \) has the probability density function (pdf) below.\[f(y) = \begin{cases} \frac{1}{25}y & 0 \leq y < 5 \\\frac{2}{5} - \frac{1}{25}y & 5 \leq y \leq 10 \\0 & y < 0 \text{ or } y > 10 \end{cases}\]**Explanation:**The piecewise function defines the probability density function of the total waiting time \( Y \):- For \( 0 \leq y < 5 \), the pdf is given by \( \frac{1}{25}y \), which indicates a linear increase in probability density. - For \( 5 \leq y \leq 10 \), the pdf is \( \frac{2}{5} - \frac{1}{25}y \), showing a linear decrease in probability density. - For \( y < 0 \) or \( y > 10 \), the pdf is 0, indicating that these waiting times are not possible.The diagram can typically be interpreted as a triangular shape, starting from zero, rising to a peak, and then descending back to zero across the interval \( [0, 10] \).

Given Information: fy=125y 0≤y<525-125y 5≤y≤10 0 y<0 or y>10

What is the probability that total waiting time is at most 4 min? What is the probability that total waiting time is between 4 and 8 min? What is the probability that total waiting time is either less than 3 min

What is the probability that total waiting time is at most 4 min? What is the probability that total waiting time is between 4 and 8 min? What is the probability that total waiting time is either less than 3 min

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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