1. The length of time required by students to complete a one-hour exam is a random variable, X, with the probability density function given by f(x) = {cx²+x, 0≤x≤1 10, elsewhere (a) Find c. (b) Find F(x) (c) Use F(x) to find the probability that randomly selected student will finish in less than 45 minutes.
1. The length of time required by students to complete a one-hour exam is a random variable, X, with the probability density function given by f(x) = {cx²+x, 0≤x≤1 10, elsewhere (a) Find c. (b) Find F(x) (c) Use F(x) to find the probability that randomly selected student will finish in less than 45 minutes.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![1. The length of time required by students to complete a one-hour exam is a random variable, \( X \), with the probability density function given by
\[
f(x) =
\begin{cases}
cx^2 + x, & 0 \leq x \leq 1 \\
0, & \text{elsewhere}
\end{cases}
\]
(a) Find \( c \).
(b) Find \( F(x) \).
(c) Use \( F(x) \) to find the probability that a randomly selected student will finish in less than 45 minutes.
(d) Find the probability that a randomly selected student needs at least 15 minutes and will finish in less than 30 minutes.
(e) Find \( \mu \) and \( \sigma \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6c9872f4-07a5-438e-9711-8d7455ed4876%2Fdb748026-5450-4224-a98a-72bd2017876a%2F5sfxbzn_processed.png&w=3840&q=75)
Transcribed Image Text:1. The length of time required by students to complete a one-hour exam is a random variable, \( X \), with the probability density function given by
\[
f(x) =
\begin{cases}
cx^2 + x, & 0 \leq x \leq 1 \\
0, & \text{elsewhere}
\end{cases}
\]
(a) Find \( c \).
(b) Find \( F(x) \).
(c) Use \( F(x) \) to find the probability that a randomly selected student will finish in less than 45 minutes.
(d) Find the probability that a randomly selected student needs at least 15 minutes and will finish in less than 30 minutes.
(e) Find \( \mu \) and \( \sigma \).
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 3 images
Similar questions
- Recommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
Numerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEYAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEY
Mathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,
