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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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
The time, T (measured in seconds), between successive hits on a website (“inter-hit time” in the rest of the problem) follows the exponential distribution with parameter 1/2. (a) What is the probability that a randomly selected inter-hit time is between 1 and 3 seconds? (b) Assume that different inter-hit times are independent of each other. A random sample of 810 inter-hit times is obtained. Give an exact symbolic expression for the probability that more than 290 of the inter-hit times in the sample are between 1 and 3 seconds? (c) Obtain a good numerical approximation for the probability from part (b)
A microprocessor that controls the tuner in color TVs fails completely at random (that is, according to the exponential distribution). Suppose that the likelihood that a microprocessor that has survived for k years fails in year k + 1 is .0036. What is the cumulative distribution function of the time until failure of the microprocessor?
Let Y be the present value random variable of a 10-year term annuity-due of 1 issued at an individual (35). Calculate its actuarial present value if (a) Mortality follows De Moivre's Law with w = 100. (b) 8 = 0.05.
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:
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)?
The time intervals between successive barges passing a certain point on a busy waterway have an exponential distribution with mean 10 minutes. (a) Find the probability that the time interval between two successive barges is less than 8 minutes. (b) Find a time interval t such that we can be 95% sure that the time interval between two successive barges will be greater than t.
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
Suppose that the probability density function of the length of computer cables is f (x) = 2x/(32) for x between 0 and 3 meters. Determine the mean of the cable length. Please enter the answer to 2 decimal places.
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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