can you please hellp me with this probllem because I don't understand this because this is getting really hard, can you please do this step by step and can you label the parts **3.1-15.** The life \( X \) (in years) of a voltage regulator of a car has the probability density function (pdf)\[f(x) = \frac{3x^2}{7^3} e^{-(x/7)^3}, \quad 0 < x < \infty.\]a. What is the probability that this regulator will last at least seven years?b. Given that it has lasted at least seven years, what is the conditional probability that it will last at least another 3.5 years?

f(x) = = 3x² 73 e-(2/7)3 0 < x <∞. a. What is the probability that this regulator will last at least seven years? b. Given that it has lasted at least seven years, what is the conditional probability that it will last at least another 3.5 years?

f(x) = = 3x² 73 e-(2/7)3 0 < x <∞. a. What is the probability that this regulator will last at least seven years? b. Given that it has lasted at least seven years, what is the conditional probability that it will last at least another 3.5 years?

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

can you please hellp me with this probllem because I don't understand this because this is getting really hard, can you please do this step by step and can you label the parts

**3.1-15.** The life \( X \) (in years) of a voltage regulator of a car has the probability density function (pdf)

\[
f(x) = \frac{3x^2}{7^3} e^{-(x/7)^3}, \quad 0 < x < \infty.
\]

a. What is the probability that this regulator will last at least seven years?

b. Given that it has lasted at least seven years, what is the conditional probability that it will last at least another 3.5 years?

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