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
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![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 \( \sigma \).
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