Explain in general terms the relationship that exists between the Poisson and exponential distribution and some example that demonstrates it
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Explain in general terms the relationship that exists between the Poisson and exponential distribution and some example that demonstrates it
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- NoneThe cost of all maintenance for a car during its first year is approximately exponentially distributed with a mean of $131. The lambda of this distribution is The probability that the cost is larger than $157 is P(x ≥ $157) = The probability that the cost is less than $97 is P(x ≤ $97) = The probability that the cost is between $121 and $143 is P($121 ≤ x ≤ $143) = The 20th percentile is cost of maintenance $Broad Explanation Please The operator of a pumping station has observed that demand for water during early afternoon hours has an approximately exponential distribution with mean 1000 cfs (cubic feet per second). a) What water-pumping capacity should the station maintain during early afternoons so that the probability that demand will be below the capacity on a randomly selected day is 0.995? b ) Of the three randomly selected afternoons, what is the probability that on at least two afternoons the demand will exceed 700 cfs?
- A test has been devised to measure a student's level of motivation during high school. The motivation scores on this test are approximatley normally distributed with a mean of 40 and a standard deviaton of 10. The higher the score the greater the motivation to do well in school. What percentage of students taking his test will score above a 50?The lifetime (in years) of a specific helicopter part follows an exponential distribution whoseexpectation is 4 years.(a) What is the probability that one of these parts will stay operational for more than 4.4 years?(b) What is the probability that one of these parts will stay operational between 2.5 and 4 years.Serial correlation, also known as autocorrelation, describes the extent to which the result in one period of a time series is related to the result in the next period. A time series with high serial correlation is said to be very predictable from one period to the next. If the serial correlation is low (or near zero), the time series is considered to be much less predictable. For more information about serial correlation, see the book Ibbotson SBBI published by Morningstar. A research veterinarian at a major university has developed a new vaccine to protect horses from West Nile virus. An important question is: How predictable is the buildup of antibodies in the horse's blood after the vaccination is given? A large random sample of horses were given the vaccination. The average antibody buildup factor (as determined from blood samples) was measured each week after the vaccination for 8 weeks. Results are shown in the following time series. Original Time Series Week Buildup Factor 2 3 4…
- A five years Business Informatics student studying at TU Wien does some temporary substitute work on the banking sector every 31 days on average, and this time follows an exponential distribution. After acquiring one of these works, its duration is also aleatoric, exponentially distributed and its mean duration is 60 daysThe money earned depends on the total number of days worked in each contract, paid at $100 daily. For unemployment periods, the student has taken out an insurance for which $50 is paid for each day on the dole. Build a queuing model to establish the mean annual income (1 year = 365 days) that the student earns. (Hint: single server, finite customer population of 1.)Serial correlation, also known as autocorrelation, describes the extent to which the result in one period of a time series is related to the result in the next period. A time series with high serial correlation is said to be very predictable from one period to the next. If the serial correlation is low (or near zero), the time series is considered to be much less predictable. For more information about serial correlation, see the book Ibbotson SBBI published by Morningstar. An Internet advertising agency is studying the number of "hits" on a certain web site during an advertising campaign. It is hoped that as the campaign progresses, the number of hits on the web site will also increase in a predictable way from one day to the next. For 10 days of the campaign, the number of hits × 105 is shown. Original Time Series Day 1 2 3 4 5 6 7 8 9 10 Hits × 105 1.3 3.5 4.4 7.2 6.8 8.3 9.0 11.3 13.1 14.7 Test ρ > 0 at the 1% level of significance. (Use 2 decimal places.) tMay is tornado season in Oklahoma. According to the National Weather Service, the Poisson rate of tornados in Oklahoma in May is 0.7 per day, based on data from 1950 to the present. The meteorologist is interested in X= the time (in days) from the start of May until the 3rd tornado to occur. Which distribution is an appropriate model for the distribution of X? Gamma Poisson Exponential Beta
- Serial correlation, also known as autocorrelation, describes the extent to which the result in one period of a time series is related to the result in the next period. A time series with high serial correlation is said to be very predictable from one period to the next. If the serial correlation is low (or near zero), the time series is considered to be much less predictable. For more information about serial correlation, see the book Ibbotson SBBI published by Morningstar.A company that produces and markets video games wants to estimate the predictability of per capita consumer spending on video games in a particular country. For the most recent 7 years, the amount of annual spending per person per year is shown here. Original Time Series Year 1 2 3 4 5 6 7 $ per capita 32.27 34.06 37.83 43.32 44.62 49.67 51.83 (a) To construct a serial correlation, we use data pairs (x, y) where x = original data and y = original data shifted ahead by one time period. Construct the data…Exponential distribution is most widely used distribution in reliability and risk assessment. The exponential distribution is closely related with the Poisson distribution which is discrete. If the number of failure per unit time is Poisson distribution then the time between failures follows exponential distribution. A system has a failure rate A = 10-4/h. What is the probability that A. it will fail before 1000 h B. it will survive at least 10,000 h C. it will fail between 1000 and 10,000 h.Suppose that the time to failure (in hours) of fans in a personal computer can be modeled by an exponential distribution with A = 0.0003. • What proportion of the fans will last at most 10,000 hours? • What proportion of the fans will last at least 7000 hours? a. 0.0498, 0.8775 Ob. NONE Oc 0.0498, 0.1225 Od.0.0502, 0.1225