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Answer: In commuting to work, a professor must first get
Chapter 4, Problem 8E(choose chapter or problem)
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 pdf
\(f(y)=\left\{\begin{array}{cl}\frac{1}{25} y & 0 \leq y<5 \\\frac{2}{5}-\frac{1}{25} y & 5 \leq y \leq 10 \\0 & y<0 \text { or } y>10\end{array}\right.\)
a. Sketch a graph of the pdf of Y.
b. Verify that \(\int_{-\infty}^{\infty} f(y) d y=1\).
c. What is the probability that total waiting time is at most 3 min?
d. What is the probability that total waiting time is at most 8 min?
e. What is the probability that total waiting time is between 3 and 8 min?
f. What is the probability that total waiting time is either less than 2 min or more than 6 min ?
Questions & Answers
QUESTION:
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 pdf
\(f(y)=\left\{\begin{array}{cl}\frac{1}{25} y & 0 \leq y<5 \\\frac{2}{5}-\frac{1}{25} y & 5 \leq y \leq 10 \\0 & y<0 \text { or } y>10\end{array}\right.\)
a. Sketch a graph of the pdf of Y.
b. Verify that \(\int_{-\infty}^{\infty} f(y) d y=1\).
c. What is the probability that total waiting time is at most 3 min?
d. What is the probability that total waiting time is at most 8 min?
e. What is the probability that total waiting time is between 3 and 8 min?
f. What is the probability that total waiting time is either less than 2 min or more than 6 min ?
ANSWER:Problem 9E