49. Suppose that a particular light bulb is advertised as having an average lifetime of 2,000hours and is known to satisfy an exponential failure law. Suppose for simplicity that thebulb is used continuously. Find the probability that the bulb lastsa. More than 3,000 hours.b. Less than 1,500 hours.c. Between 2,000 and 2,500 hours.

a) The life time of bulb follows an exponential distribution with a mean of 2000 hours. That is 1/ λ…

Answered: 49. Suppose that a particular light…

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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ASAP Very large loggers have seriousproblems keeping their skiddersrunning properly. The device fails ata rate of 3 failures every 48 hours.Suppose taht x is the time betweensnacks and is an exponentialdistribution. What is the probabilityof two or less tailures in the next 48hours?
Part 2 only please solve asap
1) Suppose that the longevity Xof a light bulb is exponential with a mean lifetime of eight years. Ifa bulb has already lasted more than 12 years, findthe probability that it will last a total of over 19 years.
A machine consists of two components: A and B. The machine needs both components to operate. As soon as one component breaks the machine fails. The time until component A breaks is an exponential with rate λA = 0.4 per year. The time until component B breaks is an exponential with rate λB = 0.4 per year. The two components are independent. Compute the probability the machine remains functional for at least another 3 years.
At a police station in a large city, calls come in at an average rate of four calls per minute. Assume that the time that elapses from one call to the next has the exponential distribution. Take note that we are concerned only with the rate at which calls come in, and we are ignoring the time spent on the phone. We must also assume that the times spent between calls are independent. This means that a particularly long delay between two calls does not mean that there will be a shorter waiting period for the next call. We may then deduce that the total number of calls received during a time period has the Poisson distribution. a. Find the average time between two successive calls. b. Find the probability that after a call is received, the next call occurs in less than ten seconds.
In 1938, a physicist named Frank Benford discovered that the number 1 appears in the first digit of random data more often than the number 2, the number 2 more often than the number 3 and so on. In general, the probability of occurrence of the first digit of a number can be written in the form of a probability function x + 1 P(X = x) = log. X a. Prove it P(X = x) = log ) untuk x = 1,2,3,4...,9 x+1 X x = 1,2,3,4..., 9 is a probability mass function 2 b. Find the cumulative distribution function of X!
suppose that the lifetime of a light bulb is exponentially distributed with mean 2 years. what is the expected value of this lifetime given that lifetime is between 1 to 3 years? e[x | 1 < x < 3] = ?
Suppose a sample consists of the numbers 1, 2, 3 ... 2n, the probability of choosing an integer k is proportional to log k. Show that the conditional probability of choosing the integer 2 given that an even number is chosen is Log 2/N log 2 + log (n!)
4. In a Exponential distribution with a λ of 5 defects per one square yard, the probability of finding a result less than 6 defects is almost 1 (100%).
2
A life insurance salesman operates on the premise that the probability that a man reaching his sixtieth birthday will not live to his sixty-first birthday is 0.05. On visiting a holiday resort for seniors, he sells 8 policies to men approaching their sixtieth birthdays. Each policy comes into effect on the birthday of the insured and pays a fixed sum on death. All 8 policies can be assumed to be mutually independent. Provide answers to the following to 3 decimal places. Part a) What is the expected number of policies that will pay out before the insured parties have reached age 61? Part b) What is the variance of the number of policies that will pay out before the insured parties have reached age 61? Part c) What is the probability that at least two policies will pay out before the insured parties have reached age 61?
The lifetime of batteries is Exponential with mean 6. Batteries are sold for $100 each. If a battery lasts less than 2 years, the manufacturer will pay the purchaser the pro rata share of the purchase price. For example if the battery lasts only 1.5 years, the manufacturer will pay the purchaser (100)(2 – 1.5)/2 = 25. What is the expected amount paid by the manufacturer per battery sold?

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