6.46 The life of a street bulb follows an exponential distribution, with an average life ß = 3 years. The bulbs are replaced whenever they fail. Out of the 1000 street bulbs installed in a city, what is the probabil- ity that at most 250 of them will need to be replaced during the first year?
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- With what kind of exponential model would doubling time be associated? What role does doubling time play in these models?On the average, 26 patrons per year come to the I.U.library to borrow the I Ching (assume that interarrival timesare exponential). Borrowers who find the book unavailableleave and never return. A borrower keeps a copy of the IChing for an average of 4 weeks.a If the library has only one copy, what is the expectednumber of borrowers who will come to borrow the IChing each year and find that the book is not available?b Suppose that each person who comes to borrow theI Ching and is unable to is considered to cost the library$1 in goodwill. A copy of the I Ching lasts two yearsand costs $11. A thief has just stolen the library’s onlycopy. To minimize the sum of purchasing and goodwillcosts over the next two years, how many copies of the IChing should be purchased?Consider the following (actual real-world) data of total cumulative coronavirus cases diagnosed in the United States by the following days: Sunday, 3/15 -- 3613 Monday, 3/16 -- 4596 Tuesday, 3/17 -- 6344 Wednesday, 3/18 -- 9197 Thursday, 3/19 -- 13779 Friday, 3/20 -- 19367 Saturday, 3/21 - 24192 Sunday, 3/22 - 33592(a) Does this data suggest exponential growth in the total number of cases diagnosed as function of the number of days that have elapsed? Explain how you would use the data to support your conclusion. (b) Let P(t) denote the total number of people in the US who have tested positive for the coronavirus on or before t days after March 15. Let P0=3613, the total number of people in the US who had tested positive for coronavirus by March 15. Then if we use an exponential growth model, P(t)=P0ekt, how would you use the above data to estimate the value of k? (c) Based on this data alone , how many total coronavirus cases would you expect to be diagnosed in the United States by…
- In 1998 El Salvador had a gini index of 54.50 and 26 years later had a gini index of 38. What does this tell us about the distribution of income throughout El Salvador?Since the data obtained as a result of 10 observations of an experiment is ∑ log niXi = 8.2431, what is the geometric mean of this experiment?A manufacturer of light bulbs finds thatthe mean lifetime of a bulb is 1200 hours. Assume the life of a bulbis exponentially distributed. In a batch of light bulbs, what is the expected time until half the light bulbs in the batch fail?
- Consider the following panel model to examine the effect of retirement on consumption expenditure, consit, of individual i over years t=1,…,3: (B1) log(consit) = β0 + β1retiredit + β2ageit + β3marriedit + β4healthit + δ1Yr2t + δ2Yr3t + ai + uit Where: retiredit is a dummy variable equal to 1 if individual i is retired on year t and 0 otherwise ageit is the individual's age in years marriedit is an indicator variable for whether the individual is married (1) or not (0) in year t healthit is an indicator variable equal to 1 if the individual is in 'good health' and 0 otherwise Yr2 is a dummy variable equal to 1 in year t=2 and 0 otherwise Yr3 is a dummy variable equal to 1 in year t=3 and 0 otherwise Using the information above, answer the following 3 questions. [i] Give two (2) examples of the kind of variables captured by the term ai in Model (B1). [ii] What is the crucial assumption we must make so that the random effects (RE) estimator is consistent? Under this assumption, why is…In deciding how many customer service representatives to hire and in planning their schedules, it is important for a firm marketing electronic typewriters to study repair times for the machines. Such a study revealed that repair times have approximately an exponential distribution with a mean of 72 minutes. In planning schedules, how much time should be allowed for each repair so that the chance of any one repair time exceeding this allowed time is only 0.15?Assuming that population growth is approximately exponential, which of the following two sets of data is most likely to represent the population (in millions) of a city over a 5-year period?
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