Reference no: EM13985410
A specific component in a cryptometer has an Exp(µ)-distributed life- time, µ > 0. If replacement is made as soon as a component fails, and if X(t) = # failures during (0, t] = # replacements during (0, t], then {X(t), t ≥ 0} is, of course, a Poisson process. Let {Vn, n ≥ 1} be these usual interreplacement times, and suppose, instead, that the nth component is replaced:
(a) After time min{Vn, a}, that is, as soon as the component fails or reaches age a, whichever comes first. Show that the replacement process is not a Poisson process.
(b) After time min{Vn, Wn}, where {Wn, n ≥ 1} is a sequence of independent, Exp(θ)-distributed random variables, θ > 0, which is indepen- dent of {Vn, n ≥ 1}. Show that the replacement process is a Poisson process and determine the intensity.
|
Problem regarding the poisson process with intensity
: M°ans waits for the bus. The waiting time, T , until a bus comes is U (0, a)- distributed. While he waits he tries to get a ride from cars that pass by according to a Poisson process with intensity λ. The probability of a passing car ..
|
|
What is the potential energy of the block
: What is the potential energy of the block before It Is released relative to the bottom of the circle? What is the kinetic energy and the speed of the block when it reaches the bottom?
|
|
What is erp system
: What is ERP system? Give a brief history of ERP system. How did ERP system bring Career Opportunities?
|
|
Problem regarding the service times independent
: The service times are independent and Exp(8)-distributed. Let Tk be the time from 9:05 until service has been completed for k of the two customers, k = 1, 2. Find E Tk for k = 1 and 2.
|
|
Poisson process and determine the intensity
: After time min{Vn, Wn}, where {Wn, n ≥ 1} is a sequence of independent, Exp(θ)-distributed random variables, θ > 0, which is indepen- dent of {Vn, n ≥ 1}. Show that the replacement process is a Poisson process and determine the intensity.
|
|
Write an essay in which you evaluate what a business
: Write an essay in which you evaluate what a business or government agency would need to consider before transferring a hardy but non indigenous species to another country.
|
|
Poisson process with an intensity
: A particle source A emits one particle at a time, according to a Poisson process with an intensity of two particles a minute. Another particle source B emits two particles at a time, according to a Poisson process with an intensity of one pair of ..
|
|
Calculate the angle in degrees
: A student stands do = 2.8 m in front of a floor-to-ceiling mirror. Her eyes are he = 1.41 m above the floor and she holds a flashlight at a distance hf = 0.8 m above the floor. Randomized Variables do=2.8m he=1.41 m hf=0.8m. Calculate the angle θ, in..
|
|
How large does radius r of the dish have to be to achieve
: How large does the radius R of the dish have to be to achieve an electric field vector amplitude of 5.7 x10-4V/m , at the receiver?
|