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The special case of the gamma distribution in which a is a positive integer n is called an Erlang distribution. If we replace b by 1/l in Expression (4.8), the Erlang pdf is
It can be shown that if the times between successive events are independent, each with an exponential distribution with parameter λ, then the total time X that elapses before all of the next n events occur has pdf f(x; λ, n).
a. What is the expected value of X? If the time (in minutes) between arrivals of successive customers is exponentially distributed with λ5 .5, how much time can be expected to elapse before the tenth customer arrives?
b. If customer interarrival time is exponentially distributed with λ = .5, what is the probability that the tenth customer (after the one who has just arrived) will arrive within the next 30 min?
c. The event {X= t} occurs iff at least n events occur in the next t units of time. Use the fact that the number of events occurring in an interval of length t has a Poisson distribution with parameter λt to write an expression (involving Poisson probabilities) for the Erlang cdf
are americas top chief executive officers ceos really worth all that money? one way to answer this question is to look
We want to determine if the proportion of people in the population who believes this is less than 0.75. What is the p-value?
Use a spreadsheet with the data below to find the all-items index numbers listed below for Years 1 and 2 with Year 0 as the base year.
The standard deviation is $10,000, can the president conclude that there is difference? At a =0.10, is he correct? The hypotheses and the claim.
She then selects a sample of 102 football players and finds that their average math SAT is 460. Use alpha =.01 to perform the appropriate hypothesis test.
The U.S. Commission of Crime wishes to estimate the fraction of crimes related to firearms in an area with one of the highest crime rates in the country.
question what type of transformation has the same effect as the composition of a reflection in x2 and then in x6?a
A new product has the following profit projections, associated probabilities, and indifference probability:
If the effective equivalent annual interest rate is 22.2%, and interest is compounded quarterly, what is the corresponding nominal annual interest rate?
Copying times average 8 minutes according to an exponential distribution. What are the operating characteristics for this system?
Country A and Country C spends about the same amount on average per person per year. Which has the greater spread?
Conduct a hypothesis test for each sample at the 0.01 level of significance and determine what action, if any should be taken.
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