Solution Found!
A gas station operates two pumps, each of which can pump
Chapter 4, Problem 14E(choose chapter or problem)
A gas station operates two pumps, each of which can pump up to 10,000 gallons of gas in a month. The total amount of gas pumped at the station in a month is a random variable Y (measured in 10,000 gallons) with a probability density function given by
\(f(y)=\left\{\begin{array}{ll} y, & 0<y<1, \\ 2-y, & 1 \leq y<2, \\ 0, & \text { elsewhere. } \end{array}\right.\)
a. Graph \(f(y)\).
b. Find \(F(y)\) and graph it.
c. Find the probability that the station will pump between 8000 and 12,000 gallons in a particular month.
d. Given that the station pumped more than 10,000 gallons in a particular month, find the probability that the station pumped more than 15,000 gallons during the month.
Questions & Answers
(1 Reviews)
QUESTION:
A gas station operates two pumps, each of which can pump up to 10,000 gallons of gas in a month. The total amount of gas pumped at the station in a month is a random variable Y (measured in 10,000 gallons) with a probability density function given by
\(f(y)=\left\{\begin{array}{ll} y, & 0<y<1, \\ 2-y, & 1 \leq y<2, \\ 0, & \text { elsewhere. } \end{array}\right.\)
a. Graph \(f(y)\).
b. Find \(F(y)\) and graph it.
c. Find the probability that the station will pump between 8000 and 12,000 gallons in a particular month.
d. Given that the station pumped more than 10,000 gallons in a particular month, find the probability that the station pumped more than 15,000 gallons during the month.
ANSWER:Step 1 of 5
Let a random variable Y with a probability density function given is by
\(F(y)=\left\{\begin{array}{cc} y, & 0<y<1 \\ 2-y, & 1 \leq y<2 \\ 0, & \text { elsewhere } \end{array}\right.\)
Our goal is:
a). We need to plot a graph f(y).
b). We need to find F(y).
c). We need to find the probability that the station will pump between 8000 and 12,000 gallons in a particular month.
d). We need to find the probability that the station pumped more than 15000 gallons during the month.
Reviews
Review this written solution for 31679) viewed: 2681 isbn: 9780495110811 | Mathematical Statistics With Applications - 7 Edition - Chapter 4 - Problem 14e
Thank you for your recent purchase on StudySoup. We invite you to provide a review below, and help us create a better product.
No thanks, I don't want to help other students