The probabilityfunction for the time to failure in years of the engine on a car is given byf(x) = 0.3-0.04x 0≤x≤ 10 yeara. If the car undergoes preventive maintenance every 4 months that restore it to as good as new condition, determine its reliability at the endof 2 years' warranty.If 022/0densityb. Compute the meantime to failure under the preventive maintenance plan in part (a)

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Answered: The probability density function for…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Consider an item with time to failure T that has a Weibull distribution with shape parameter 2.25 and scale parameter 0.0004 per hours. When the item fails it is repaired to an as good as new condition. The repairtime (downtime) D has a lognormal distribution with parameters 1.5 and 0.42. The item is supposed to be in continuous operation. (a) Find the average availability of the item. (b) A preventive maintenance task that takes 5 hours is performed every 300 hours. Find the operational availability of the item.
A person arrives at the side of a single lane, one way street as a car passes by. Consider this time as time 0. There is no traffic lights and no pedestrian lanes in the nearby area. He stands there watching cars pass by. The number of cars to pass by within a period of time cane be modeled using a poison distribution. Suppose the cars pass by the person at a rate of 4.5 cars per minute. Assume that the cars pass by instantaneously. what is the probability that no cars pass by him within a 2 minute window b) if the person had to guess how many cars would pass by in the next five minutes, what number should he guess? Why? c) what is the distribution for the time until the first car passes by him(time is continuous). What is the expected time until the first car passes by him?
Suppose X has an exponential distribution with mean equal to 12. Determine the following: (a) P(X > 10) (Round your answer to 3 decimal places.) (b) P(X > 20) (Round your answer to 3 decimal places.) (c) P(X < 30) (Round your answer to 3 decimal places.) (d) Find the value of x such that P(X
Let X1 and X2 be IID exponential with parameter > 0. Determine the distribution ofY = X1=(X1 + X2).
Q5 Find the variance for the PDF px(x) = e-«/2, x > 0.
Suppose that X follows a lognormal distribution with w^2=4 and E(X)=10,000 a. Find the parameter theta for the distribution. Use 4 digits after the decimal point: b. Find the standard deviation of the process: Use 4 digits after the decimal point:
The daily price of orange juice 30-day futures is normally distributed. InMarch through April 2007, the mean was 145.5 cents per pound, and standarddeviation = 25.0 cents per pound.4 Assuming the price is independent from day today, find P (x < 100) on the next day.
An accident-prone motorist has two tragic accidents with two weeks between rooms. The 'waiting time' (measured in days) between two accidents can be approximately approximated as exponentially distributed with unknown expected value µ. Determine a 90% condensation interval for µ. Please explin so I understand to ba able to solve similar kind of questions..
Assume the time required to fully recharge an electric car is uniformly distributed between 160 and 220 minutes. What is the expected charge time, E(x)?
Suppose you simulate the price path of stock HHF using a geometric Brownian motion model with µ = 0.1, o = 0.2, and time step At = 1/52 (weekly). Let St be the price of the stock at time t. If So = 100, and the first simulated (randomly selected) standard normal variable is e = -0.591, what is the simulated return over the next week? (a) -0.061 (b) -0.015 (c) 0.061 (d) -0.093
The time until a chemical reaction is complete (in milliseconds) is approximated by cumulative distribution function F(2) = { ,"ani 0lz The probability that a reaction completes within 400 milliseconds is
The lifetime in months of a transistor in a certain application is random with probabilitydensity functionf (t) =0.1e0.1t ,t > 0=0, t ≤ 0a. Find the mean lifetime.b. Find the cumulative distribution function of the lifetime.

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