1. Use a software to simulate 1,000 random numbers from an Exponential distribution whose mean is 50, i.e., X - Exp(50). Verify the memory-less property of the Exponential distribution using your simulated data through the following steps: (a) Estimate P(X > t) for t = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50. (b) Estimate P(X > t + 10 | X > 10) for t = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50. Plot the estimated probabilities in (b) against those in (a) in one graph. (c) Estimate P(X > t + 20 | X > 20) for t = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50. Plot the estimated probabilities in (c) against those in (b) in one graph. (d) Summarize your findings.
1. Use a software to simulate 1,000 random numbers from an Exponential distribution whose mean is 50, i.e., X - Exp(50). Verify the memory-less property of the Exponential distribution using your simulated data through the following steps: (a) Estimate P(X > t) for t = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50. (b) Estimate P(X > t + 10 | X > 10) for t = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50. Plot the estimated probabilities in (b) against those in (a) in one graph. (c) Estimate P(X > t + 20 | X > 20) for t = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50. Plot the estimated probabilities in (c) against those in (b) in one graph. (d) Summarize your findings.
MATLAB: An Introduction with Applications
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Chapter1: Starting With Matlab
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![1. Use a software to simulate 1,000 random numbers from an Exponential distribution whose mean is 50,
i.e., X - Exp(50). Verify the memory-less property of the Exponential distribution using your simulated
data through the following steps:
(a) Estimate P(X > t) for t = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50.
(b) Estimate P(X > t + 10 | X > 10) for t = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50. Plot the estimated
probabilities in (b) against those in (a) in one graph.
(c) Estimate P(X > t + 20 | X > 20) for t = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50. Plot the estimated
probabilities in (c) against those in (b) in one graph.
(d) Summarize your findings.
2. Round up the above simulated random number to the smallest integer that is no less than the random
number, i.e., let Y = [X]. For example, [0.01] = 1, [1.0] = 1, and [5.62] = 6. Repeat the four parts in
Problem 1 using the transformed data set. What is this distribution?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcbb74936-c73d-423e-b5c0-4a7ff906acfc%2Faefb2656-2a63-4052-bcea-a399fbc72359%2F0ygvign_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Use a software to simulate 1,000 random numbers from an Exponential distribution whose mean is 50,
i.e., X - Exp(50). Verify the memory-less property of the Exponential distribution using your simulated
data through the following steps:
(a) Estimate P(X > t) for t = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50.
(b) Estimate P(X > t + 10 | X > 10) for t = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50. Plot the estimated
probabilities in (b) against those in (a) in one graph.
(c) Estimate P(X > t + 20 | X > 20) for t = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50. Plot the estimated
probabilities in (c) against those in (b) in one graph.
(d) Summarize your findings.
2. Round up the above simulated random number to the smallest integer that is no less than the random
number, i.e., let Y = [X]. For example, [0.01] = 1, [1.0] = 1, and [5.62] = 6. Repeat the four parts in
Problem 1 using the transformed data set. What is this distribution?
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