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Problem 5 You purchase a certain product. The manual states that the lifetime T of the product, defined as the amount of time (in years) the product works properly until it breaks down, satisfies P(T t) = e- for all t 2 0. %3D For example, the probability that the product lasts more than (or equal to) 2 years is P(T > 2) = e- = 0.6703. %3D a. This is an example of a continuous probability model. Write down the sample space S. b. Check that the statement in the manual makes sense by finding P(T > 0) and lim, 00 P(T > t). c. Also check that if t < t2, then P(T >t1) > P(T>t2). Why does this need to be true?

Problem 5 You purchase a certain product. The manual states that the lifetime T of the product, defined as the amount of time (in years) the product works properly until it breaks down, satisfies P(T t) = e- for all t 2 0. %3D For example, the probability that the product lasts more than (or equal to) 2 years is P(T > 2) = e- = 0.6703. %3D a. This is an example of a continuous probability model. Write down the sample space S. b. Check that the statement in the manual makes sense by finding P(T > 0) and lim, 00 P(T > t). c. Also check that if t < t2, then P(T >t1) > P(T>t2). Why does this need to be true?

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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Problem 5 You purchase a certain product. The manual states that the lifetime T of the product, defined as the amount of time (in years) the product works properly until it breaks down, satisfies P(T > t) = e-} for all t > 0. For example, the probability that the product lasts more than (or equal to) 2 years is P(T > 2) = e¯† = 0.6703. %3D a. This is an example of a continuous probability model. Write down the sample space S. b. Check that the statement in the manual makes sense by finding P(T > 0) and lim,0 P(T > t). c. Also check that if tį < t2, then P(T >t1) > P(T> t2). Why does this need to be true?
Transcribed Image Text:Problem 5 You purchase a certain product. The manual states that the lifetime T of the product, defined as the amount of time (in years) the product works properly until it breaks down, satisfies P(T > t) = e-} for all t > 0. For example, the probability that the product lasts more than (or equal to) 2 years is P(T > 2) = e¯† = 0.6703. %3D a. This is an example of a continuous probability model. Write down the sample space S. b. Check that the statement in the manual makes sense by finding P(T > 0) and lim,0 P(T > t). c. Also check that if tį < t2, then P(T >t1) > P(T> t2). Why does this need to be true?
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