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(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
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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Question #8
**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 \( x = 0, 1, 2, 3, \ldots, 16 \).
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,

  lambda equals 0.2 t equals 30

Thus, the parameter of X is,

lambda t equals 0.2 asterisk times 30 equals 6

P left parenthesis X equals x right parenthesis equals fraction numerator e to the power of negative 6 end exponent 6 to the power of x over denominator x factorial end fraction


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