(a) Construct a probability distribution for the random variable X, assuming it follows a Poisson process with λ=0.2 and t=30. This is the probability distribution of X before the advertising. Remember that x = 0,1,2,3,...,16.
(a) Construct a probability distribution for the random variable X, assuming it follows a Poisson process with λ=0.2 and t=30. This is the probability distribution of X before the advertising. Remember that x = 0,1,2,3,...,16.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Question #8

Transcribed Image Text:**Drive-Through Car Arrival Study**
Cars arrive at a certain restaurant's drive-through at a rate of 0.2 cars per minute between the hours of 11:00 P.M. and 1:00 A.M. on Saturday evening. The restaurant begins an advertising blitz that touts its late-night service. After one week of advertising, the restaurant’s officials count the number of cars, \( X \), arriving at the restaurant's drive-through between the hours of 12:00 midnight and 12:30 A.M. for 198 of its restaurants. The results are shown in the following table. Use the table to answer parts (a) through (c).
**Restaurant Car Arrival Frequency**
| \( x \) (number of cars arriving) | Frequency |
|-----------------------------------|-----------|
| 1 | 4 |
| 2 | 5 |
| 3 | 14 |
| 4 | 25 |
| 5 | 26 |
| 6 | 25 |
| 7 | 26 |
| 8 | 27 |
| 9 | 20 |
| 10 | 15 |
| 11 | 6 |
| 12 | 2 |
| 13 | 2 |
| 14 | 2 |
| 15 | 2 |
| 16 | 2 |
**Task:**
(a) Construct a probability distribution for the random variable \( X \), assuming it follows a Poisson process with \( \lambda = 0.2 \) and \( t = 30 \). This is the probability distribution of \( X \) before the advertising. Remember that \( x = 0, 1, 2, 3, \ldots, 16 \).
Expert Solution

Step 1: Determine the given data in the question
Let X be the random variable that the number of cars arriving at the restaurant's drive-through.
Given that,
Thus, the parameter of X is,
Step by step
Solved in 3 steps with 3 images
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