Depend on the number, The policy of searching for a ?xed

Depend on the number

Assignment Help Basic Statistics

Reference no: EM131005862

The number of missing items in a certain location, call it X, is a Poisson random variable with mean λ. When searching the location, each item will independently be found after an exponentially distributed time with rate μ. A reward of R is received for each item found, and a searching cost of C per unit of search time is incurred. Suppose that you search for a ?xed time t and then stop.

(a) Find your total expected return.

(b) Find the value of t that maximizes the total expected return.

(c) The policy of searching for a ?xed time is a static policy. Would a dynamic policy, which allows the decision as to whether to stop at each time t, depend on the number already found by t be bene?cial?

Reference no: EM131005862

Questions Cloud

Events of a nonhomogeneous poisson process : Let T1, T2, ... denote the interarrival times of events of a nonhomogeneous Poisson process having intensity function λ(t).

Determine the economic service life of the sifter : The operating cost is expected to follow the series described by 40,000 + 10,000k, where k is the number of years since it was purchased (k = 1 through 7). The salvage value is estimated to be $30,000 for years 1 and 2 and $20,000 for years 3 thro..

Determine the economic service life of the equipment : The salvage value of the equipment is expected to be $140,000 for the first 3 years, but due to obso- lescence, it won't have a significant value after that. At an interest rate of 10% per year, determine the economic service life of the equipment..

Independent of the arrival process : The service times of the arrivals are independent exponential random variables with rate μ, and are independent of the arrival process. Customers depart the system when their service ends. Let N be the number of arrivals before the ?rst departure.

Depend on the number : The policy of searching for a ?xed time is a static policy. Would a dynamic policy, which allows the decision as to whether to stop at each time t, depend on the number already found by t be bene?cial?

Distribution of the time : What is the distribution of the time at which the last rider departs the car? Suppose the last rider departs the car at time t. What is the probability that all the other riders are home at that time?

Distributed according to a poisson process : Policyholders of a certain insurance company have accidents at times distributed according to a Poisson process with rate λ. The amount of time from when the accident occurs until a claim is made has distribution G.

Number of customers in the system : 1. Consider an in?nite server queuing system in which customers arrive in accordance with a Poisson process with rate λ, and where the service distribution is exponential with rate μ. Let X(t) denote the number of customers in the system at time t..

Problem regarding the independent increments : (a) Find P{N(t) = n}. (b) Is {N(t)} a Poisson process? (c) Does {N(t)} have stationary increments? Why or why not? (d) Does it have independent increments? Why or why not?

User Account

All Pages