A factory produced two equal size batches of radios. All the radios look alike, but the lifetime of a radio inthe first batch is continuous and uniformly distributed over the interval from 0 to 3 years, while the lifetimeof a radio in the second batch is exponentially distributed with parameter λ=1. Answer the twoquestions below.Suppose Alicia bought a radio and after 4 years it is still working. What is the conditional probability it willstill work for at least 5 more years?Now suppose Venkatesh bought a radio and after 1 year it is still working. What is the conditional probabilityit will work for at least 5 more years?For symbolic expressions, all numbers must be rational: use 1/10 instead of 0.1.Ans1: symbolic expressionAns2: symbolic expression

Let T1 denote the first batch.Let T2 denote the second batch.

Answered: A factory produced two equal size…

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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question 8
The lifetime T (in years) for a particular type of electric toothbrush is assumed to have the probability density f given by t 0 ≤ t ≤6 f(t) = {+ 3 18 otherwise.
PART C. 1. James is an operator of a machine that uses 16 batteries. Because it has so many, it does not shut off until half of the batteries are dead. a. All batteries are independent and have uniformly distributed lifetimes on the interval [ 0, 1 2] years. Find the probability that the machine shuts before 1 years of work? b. What is the expected time when the 5th and the 8th battery die?
Question 24
In major league baseball, a no hitter is a game in which a pitcher, or pitchers, doesn't give up any hits throughout the game. No hitters occur at a rate of about three per season. Assume that the duration of time between no hitters is exponential. a. what is the probability that an entire season elapses with a single no-hitter? b. If an entire season elapses without any no hitters, what is the probabilty that there are no no hitters in the following season? c. What is the probabilty that there are more than 3 no hitters in a single season?
In the game of roulette, a player can place a $9 bet on the number 29 and have a probability of winning. If the metal ball lands on 29, the player gets to keep the 38 1 $9 paid to play the game and the player is awarded an additional $315. Otherwise, the player is awarded nothing and the casino takes the player's $9, Find the expected value E(x) to the player for one play of the game. If x is the gain to a player in a game of chance, then E(x) is usually negative. This value gives the average amount per game the player can expect to lose. The expected value is $.5 (Round to the nearest cent as needed.)
1. Suppose you are a technician, whose repair time on a given job is said to follow an exponential distribution with expected time θ = 3 hours. You have 5 independent jobs lined up (you complete them sequentially, one by one). a. What is the probability of taking exactly 2 hours to finish a given job? b. What is the probability it will take more than 2 hours on a given job? c. You are on a given job and you already have been working for 1 hour. What is the probability it will at least an additional 2 hours to complete this job?
Suppose that we have test for lung cancer, which correctly identifies those with the cancer 70 % of the time, and mistakenly identifies those without the cancer 5 % of the time. In the cohort of interest, the rate of this cancer is somewhat low: 0.9 %. Find the probability -- a number between 0 and 1 -- that someone diagnosed (testing positive) with this test actually has lung cancer.
A blockchain-based business received consensus validation via two different systems A and B. The time between validations for each validation system in a typical day is known to be exponentially distributed with a mean of 3.2 seconds. Both systems operate independently. Given the above distribution, the probability that no validation will be received from system A in a 5-second period is (expressed your answer in 4 decimal places). Likewise, the probability that no validation will be received from both systems in a 5-second period is (expressed your answer in 4 decimal places). If X denotes the number of validations in a 5-second interval. Then, X is a Poisson random variable with the lambda is equal to (expressed your answer in 4 decimal places). Then, the probability that both systems receive two validations between 10 and 15 seconds after the site is (expressed in 4 decimal places). officially open for business is
A company that explores for oil in the ocean is considering two new sites, A and B. The exploration will take the entire year. The company estimates the probability of finding oil is 0.19 at site A and 0.03 at site B. The sites are far enough apart so that whether or not oil is found at one site is independent of it being found at the other. Round your answers to three decimal places, and use four decimal places in any interim calculations. Find the probability that the company will find oil at both sites: .006 Hint: Try making a probability table. only one of the sites: 163 neither of the sites: least one of the sites:
Q. No. 5:Discuss the components of time series. b)There are five flights daily from Pittsburgh via US Airways into the Bradford Regional Airport in Bradford, Pennsylvania. Suppose the probability that any flight arrives late is 0.20. What is the probability that none of the flights are late today? What is the probability that exactly one of the flights is late today?
Question 4 Suppose that in a population of twins, males (M) and females (F) are equally likely to occur and that the probability that twins are identical is 0. If twins are not identical, their genders are independent (if they are identical, their genders are the same). (i) Show that, ignoring birth order, P(MM) = P(FF) = (1+0)/4 and P(MF) = (1–0)/2. (ii) Suppose that n twins are sampled. It is found that n₁ are MM, n2 are FF, and në are MF, but it is not known which twins are identical. Find the maximum likelihood estimator of 0.

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