3. Your roommate thinks that, because you're an ECE major, it's your job to change lightbulbs. You buy a bulb. Its average lifetime is rated for 10 years. Model the actuallifetime L as an exponential random variable.(a)What is the probability that it will last longer than 5 years, i.e. P(L 2 5)?(b)After 2 years, it still hasn't burned out. Given that, what is the probabilitythat it will last 5 years beyond that, i.e. P(L 2 2+5|L 2 2)?Compare your answers in (a) and (b) and explain why they support(c).callıng the exponential R.V. "memoryless".

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Answered: 3. Your roommate thinks that, because…

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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Question 7. [5] Vodacom, uses a large number of common batteries in one of its most popular lines of phones. After testing a large number of them, they found that the average time to failure is 1/2, 8000 hours. a) What is the probability that a component will fail within 1500 hours? b. What is the probability that a component will fail after 8800 hours?
QUESTION 3 Data on a survey of 80 magazine subscribers showed that 32 subscribers rented a car during the past 12 months for business reasons, 40 subscribers rented a car during the past 12 months for personal reasons, and 24 subscribers rented a car during the past 12 months for both business and personal reasons. 3.1. What is the probability that a subscriber rented a car during the past 12 months for business reasons? 3.2. What is the probability that a subscriber rented a car during the past 12 months for personal reasons? 3.8. What is the probability that a subscriber rented a car during the past 12 months for both business and personal reasons? S.A. What is the probability that a subscriber rented a car during the past 12 months for business or personal reasons? 8.5. What is the probability that a subscriber rented a car during the past 12 months for business reasons given that the subscriber rented a car for personal reasons?
Q. 1 t is estimated that 809% of emails are spam emails. Some software has been applied to filter these spam emails before they reach our inbox. A certain brand of software claims that it can detect 99% of spam emails, and the probability for a false positive (a non-spam email detected as spam) is 5%. Now if an email is detected as spam, then what is the probability that it is in fact a non-spam email? event A: email is spam; event B: email is detected as spam. Assume that
I need help with this problem! Suppose that it snows in Greenland an average of once every 26 days, and when it does, glaciers have a 28% chance of growing. When it does not snow in Greenland, glaciers have only a 6% chance of growing. What is the probability that it is snowing in Greenland when glaciers are growing? (Round your answer to four decimal places.)
When a bus service reduces fares, a particular trip from New York City to Albany, New York, is very popular. A small bus can carry four passengers. The time between calls for tickets is exponentially distributed with a mean of 20 minutes. Assume that each caller orders one ticket. What is the probability that the bus is filled in less than 3 hours from the time of the fare reduction? Round your answer to 4 decimal places. i
The useful life of Johnson rods for use in a particular vehicle follows an exponential distribution with an average useful life of 5.2 years.You have a three-year warranty on your vehicle’s Johnson rod. What is the probability that the Johnson rod doesn’t fail before then? That is, what is the probability that its useful life doesn’t end before three years?b.If the vehicle manufacturer wants to limit the number of claims on the three-year warranty to 20%, what should the average useful life of the Johnson rod be?
vm 6.2 10 The table summarizes results from 976 pedestrian deaths that were caused by automobile accidents. DriverIntoxicated? Pedestrian Intoxicated? Yes No Yes 41 85 No 219 631 If one of the pedestrian deaths is randomly selected, find the probability that the pedestrian was intoxicated or the driver was not intoxicated.Report the answer as a percent rounded to one decimal place accuracy.
#13
Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 250 numerical entries from the file and r = 60 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1. Test the claim that p is less than 0.301 by using α = 0.01. What does the area of the sampling distribution corresponding to your P-value look like? a. The area in the right tail of the standard normal curve. b. The area not including the right tail of the standard normal curve.…
New spark plugs have just been installed in a small airplane with a two-cylinder engine. For each spark plug, the probability that it is defective and will fail during its first 20 minutes of flight is 1/1,000, independent of the other spark plugs.(a) What is the probability that none of the two spark plugs will fail during the first 20 minutes of flight? (Round your answer to four decimal places.)(b) What is the probability that at least one of the spark plugs will fail? (Round your answer to four decimal places.)
Answer question 2 parts A,B and C . Math statistics

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