An article suggests the uniform distribution on the interval (8.5, 18) as a model for depth (cm) of the bioturbation layer in sediment in a certain region. (a) What are the mean and variance of depth? (Round your variance to two decimal places.) mean variance (b) What is the cdf of depth? x < 8,5 F(x) = 8.5 sx < 18 1 18 S X (c) What is the probability that observed depth is at most 10? (Round your answer to four decimal places.) What is the probability that observed depth is between 10 and 15? (Round your answer to four decimal places.) (d) What is the probability that the observed depth is within 1 standard deviation of the méan value? (Round your answer to four decimal places.) What is the probability that the observed depth is within 2 standard deviations of the mean value?
An article suggests the uniform distribution on the interval (8.5, 18) as a model for depth (cm) of the bioturbation layer in sediment in a certain region. (a) What are the mean and variance of depth? (Round your variance to two decimal places.) mean variance (b) What is the cdf of depth? x < 8,5 F(x) = 8.5 sx < 18 1 18 S X (c) What is the probability that observed depth is at most 10? (Round your answer to four decimal places.) What is the probability that observed depth is between 10 and 15? (Round your answer to four decimal places.) (d) What is the probability that the observed depth is within 1 standard deviation of the méan value? (Round your answer to four decimal places.) What is the probability that the observed depth is within 2 standard deviations of the mean value?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![An article suggests the uniform distribution on the interval (8.5, 18) as a model for depth (cm) of the bioturbation layer in sediment in a certain region.
(a) What are the mean and variance of depth? (Round your variance to two decimal places.)
- Mean: [ ]
- Variance: [ ]
(b) What is the cdf of depth?
\[
F(x) =
\begin{cases}
0 & \text{if } x < 8.5 \\
& 8.5 \le x < 18 \\
1 & \text{if } 18 \le x
\end{cases}
\]
(c) What is the probability that observed depth is at most 10? (Round your answer to four decimal places.)
- Probability: [ ]
What is the probability that observed depth is between 10 and 15? (Round your answer to four decimal places.)
- Probability: [ ]
(d) What is the probability that the observed depth is within 1 standard deviation of the mean value? (Round your answer to four decimal places.)
- Probability: [ ]
What is the probability that the observed depth is within 2 standard deviations of the mean value?
- Probability: [ ]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb4fac401-f688-4a8e-b637-a2500ce6ac46%2Fc597de34-9d01-4b7c-b349-076049047928%2Fs0224z_processed.jpeg&w=3840&q=75)
Transcribed Image Text:An article suggests the uniform distribution on the interval (8.5, 18) as a model for depth (cm) of the bioturbation layer in sediment in a certain region.
(a) What are the mean and variance of depth? (Round your variance to two decimal places.)
- Mean: [ ]
- Variance: [ ]
(b) What is the cdf of depth?
\[
F(x) =
\begin{cases}
0 & \text{if } x < 8.5 \\
& 8.5 \le x < 18 \\
1 & \text{if } 18 \le x
\end{cases}
\]
(c) What is the probability that observed depth is at most 10? (Round your answer to four decimal places.)
- Probability: [ ]
What is the probability that observed depth is between 10 and 15? (Round your answer to four decimal places.)
- Probability: [ ]
(d) What is the probability that the observed depth is within 1 standard deviation of the mean value? (Round your answer to four decimal places.)
- Probability: [ ]
What is the probability that the observed depth is within 2 standard deviations of the mean value?
- Probability: [ ]
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