Substitution that a solution of this infinite system

Reference no: EM131129183

Suppose that f(x, t) is the probability of getting x successes during a time interval of length t when (i) the probability of a success during a very small time interval from t to t + ?t is α · ?t, (ii) the probability of more than one success during such a time interval is negligible, and (iii) the probability of a success during such a time interval does not depend on what happened prior to time t.

(a) Show that under these conditions

and hence that

(b) Show by direct substitution that a solution of this infinite system of differential equations (there is one for each value of x) is given by the Poisson distribution with λ = αt.

Reference no: EM131129183

Questions Cloud

Calculating all the values of a poisson distribution : When calculating all the values of a Poisson distribution, the work can often be simplified by first calculating p(0; λ) and then using the recursion formula

What is the mean volume of an average human cheek cell : What is the mean volume of an average human cheek cell in µm^3 ? Use the formula for a cylinder - How does the volume of an Elodea cell compare to the volume of a human cheek cell? What is their ratio?

Identify key behavioral and environmental risk factors : Describe and justify the selection of at least two theories of health behavior that can be used to address the behavior problem (the theories should be at different levels-i.e., individual, interpersonal, community).

Would source code be handled differently than documentation : How will two developers be precluded from making different changes to the same SCI at the same time?

Substitution that a solution of this infinite system : Suppose that f(x, t) is the probability of getting x successes during a time interval of length t when (i) the probability of a success during a very small time interval from t to t + ?t is α · ?t, (ii) the probability of more than one success dur..

Identify the amount that should be transferred out of work : Using the FIFO method, prepare a process cost report for April. Identify the amount that should be transferred out of the Work in Process Inventory account, and state where those dollars should be transferred.

Explain why energy is released when atp is hydrolyzed : Explain why energy is released when ATP is hydrolyzed and why energy is absorbed when ATP is formed from ADP and Pi.

Distribution function of a poisson random variable : This result is important because values of the distribution function of a Poisson random variable may thus be obtained by referring to a table of incomplete gamma functions.

Experiencing cutbacks in funding and revenues : Hargrove Hospital is experiencing cutbacks in funding and revenues. One suggestion for saving money is to eliminate one of its two birthing stations. Compared to the current situation, how much will be saved per year by using the optimum number of bi..

User Account

All Pages