The image displays a problem statement and three graphs related to exponential probability distributions.**Problem Statement:**The time between arrivals of vehicles at a particular intersection follows an exponential probability distribution with a mean of 10 seconds.(a) Sketch this exponential probability distribution.**Graphs Description:**1. **Graph on the Left:** - Y-axis is labeled as $ f(x) $ ranging from 0 to 0.15. - X-axis is labeled as $ x $ ranging from 0 to 30. - The graph shows an exponentially decreasing curve starting from approximately 0.05 at $ x = 0 $ and approaching 0 as $ x $ increases to 30. - The shaded region under the curve is in blue.2. **Middle Graph:** - Y-axis is labeled as $ f(x) $ ranging from 0 to 0.15. - X-axis is labeled as $ x $ ranging from 0 to 30. - The graph shows a steep exponentially decreasing curve starting from 0.15 at $ x = 0 $ and approaching 0 as $ x $ increases to 30. - The shaded region under the curve is in blue.3. **Graph on the Right:** - Y-axis is labeled as $ f(x) $ ranging from 0 to 0.15. - X-axis is labeled as $ x $ ranging from 0 to 30. - The graph shows an exponentially decreasing curve starting from approximately 0.10 at $ x = 0 $ and approaching 0 as $ x $ increases to 30. - The shaded region under the curve is in blue.Each graph represents a different exponential probability distribution function, which decays over time as represented by the variable $ x $. (b) What is the probability that the arrival time between vehicles is 10 seconds or less? (Round your answer to four decimal places.)[Input box](c) What is the probability that the arrival time between vehicles is 6 seconds or less? (Round your answer to four decimal places.)[Input box with answer: 0.4512 ✔️](d) What is the probability of 30 or more seconds between vehicle arrivals? (Round your answer to four decimal places.)[Input box with answer: 0.0498 ✔️]

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The time between arrivals of vehicles at a particular intersection follows an exponential probability distribution with a mean of 10 seconds. (a) Sketch this exponential probability distribution. fix) f(x) fix) 0.15 0.15 0.15 0.10 0.10 0.10 0.05 0.05 0.05 5 10 15 20 25 30 10 15 20 25 30 5 10 15 20 25 30 f(x) 0.15 0.10 0.05 5 10 15 20 25 30

The time between arrivals of vehicles at a particular intersection follows an exponential probability distribution with a mean of 10 seconds. (a) Sketch this exponential probability distribution. fix) f(x) fix) 0.15 0.15 0.15 0.10 0.10 0.10 0.05 0.05 0.05 5 10 15 20 25 30 10 15 20 25 30 5 10 15 20 25 30 f(x) 0.15 0.10 0.05 5 10 15 20 25 30

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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Concept explainers

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!

Question

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The image displays a problem statement and three graphs related to exponential probability distributions.

**Problem Statement:**

The time between arrivals of vehicles at a particular intersection follows an exponential probability distribution with a mean of 10 seconds.

(a) Sketch this exponential probability distribution.

**Graphs Description:**

1. **Graph on the Left:**
- Y-axis is labeled as $ f(x) $ ranging from 0 to 0.15.
- X-axis is labeled as $ x $ ranging from 0 to 30.
- The graph shows an exponentially decreasing curve starting from approximately 0.05 at $ x = 0 $ and approaching 0 as $ x $ increases to 30.
- The shaded region under the curve is in blue.

2. **Middle Graph:**
- Y-axis is labeled as $ f(x) $ ranging from 0 to 0.15.
- X-axis is labeled as $ x $ ranging from 0 to 30.
- The graph shows a steep exponentially decreasing curve starting from 0.15 at $ x = 0 $ and approaching 0 as $ x $ increases to 30.
- The shaded region under the curve is in blue.

3. **Graph on the Right:**
- Y-axis is labeled as $ f(x) $ ranging from 0 to 0.15.
- X-axis is labeled as $ x $ ranging from 0 to 30.
- The graph shows an exponentially decreasing curve starting from approximately 0.10 at $ x = 0 $ and approaching 0 as $ x $ increases to 30.
- The shaded region under the curve is in blue.

Each graph represents a different exponential probability distribution function, which decays over time as represented by the variable $ x $.

(b) What is the probability that the arrival time between vehicles is 10 seconds or less? (Round your answer to four decimal places.)

[Input box]

(c) What is the probability that the arrival time between vehicles is 6 seconds or less? (Round your answer to four decimal places.)

[Input box with answer: 0.4512 ✔️]

(d) What is the probability of 30 or more seconds between vehicle arrivals? (Round your answer to four decimal places.)

[Input box with answer: 0.0498 ✔️]

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