Problem. Suppose that the lifetime (x) of certain modelwith a mean life of 5 years"a. What is the probability distribution of the life of the car battery ?b. Plot the probability density function, f(x) versus the lifetime of the car battery (x)C. What is the probability that the life of the battery will be greater than 2 years?d. What is the probability that the life of the battery is greater than 2 years but less than 4 years?What is the var(x)?car battery follows an exponential distributione.

Solution As per guidelines we answer the first three subparts only.

Answered: Problem. Suppose that the lifetime (x)…

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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6. The magnitude (Richter scale) of earthquake along a Taiwanese fault is exponentially distributed, with A= (1/2.5). What is the probability of an earthquake exceeding magnitude 6.4? There is 1 earthquake per year (on average) along the fault with magnitude greater than 5.5. Given this, what is the probability of an earthquake during the year that exceeds magnitude 7.2?
22. The life X in months of a certain light bulb is a random variable with exponential density. What is the probability that the light bulb will have a life span between 25 and 30 months if its average life is 20 months?
The cost of all maintenance for a car during its first year is approximately exponentially distributed with a mean of $204. a. The lambda of this distribution is b. The probability that the cost is larger than $238 is P(x > $238) = c. The probability that the cost is less than $76 is P(x s $76) = d. The probability that the cost is between $185 and $244 is P($185 s x < $244) = e. The 61st percentile is cost of maintenance s
Assume that the lifetime of a certain component has an exponential distribution with mean 5 (and that time is measured in years). a. What is the standard deviation of lifetimes? b. What is the probability that a component lasts longer than 10 years? c. What is the probability that a component will function for at least 10 years, given that it has already function for 3 years?
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The time to first failure X of the software of a medical linear acceleratormay be modeled normal with μ = 1100 hours and σ = 50 hours.
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3. Which exponential probability density has mean u = ?
Students arrive one at a time, completely at random, to an advice clinic at a rate of10 per hour. Students take on average 5 minutes of advice but there is wide variation inthe time they need; this variation may be well modeled by the exponential distribution.b. Again assuming one advisor, what is the probability that there are more than tenstudents in the clinic at a random point in time? What is the probability that the timespent in the clinic exceeds 30 minutes?.
3. The level of impurity (in percent) in the product of a certain chemical process is a random variable with probability density function 3 64 -x²(4 - x) 0 0 < x < 4 otherwise a. What is the probability that the impurity level is greater than 3%? b. What is the probability that the impurity level is between 2% and 3%? c. Find the mean impurity level. d. Find the variance of the impurity levels.
The life X (in hours) of a battery in constant use is a random variable with exponential density. What is the probability that the battery will last more than 12 hours (h) if the average life is 8 h?

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