1. T

    Probability That A Woman Will Give Birth, Word Problem

    The probability that a woman will give birth to a girl during any given pregnancy is 48%. Please check answer to A. a.) What is the probability that a couple planning to have four children will have exactly one girl? P(x) = C(n,x) * P^x * Q^n-x P(x) = C(4,1) * 0.48^1 * 0.52^3 P(x) = 0.27...
  2. K

    Birth rate of a population question

    The birth rate 'Beta (t)' of a population 'P (t)' decreases exponentially with time, so that 'Beta (t)'= 'Beta0 exp^(-Alpha t)', where 'Alpha, Beta > 0'. Therefore the population dynamics are governed by the differential equation, (dP/dt)= Beta (t)P, P(0)=Po Solve the above initial value...
  3. I

    Birth Process

    I have been trying to figure this problem out for a few days now and don't seem to know where to start. Consider a population made of a fixed number (N) of people. At time t=0 there is only one infected individual and N-1 susceptible people in the population. When you get infected, you remain...
  4. K

    birth rate DE problem

    Dear Sir I would be grateful if you can help me to solve the the below questions The answers are: a)31.54 million b) 13.44 million c)1179 million thanks Kingsman
  5. K

    Birth and Death Processes / First-order difference equation question

    Hi Everyone, I have become stuck on the following problem. Here is the statement: In a simple birth and death process, the birth rates are and the death rates are for . The birth and death rates are 0 elsewhere. The parameters and are positive and satisfy . Let . Show that satisfies...
  6. C

    Pure birth process

    Let X(t) be a pure birth process with X(0) = 1 and parameters \lambda_{k}=k Let p_{n}(t)=P(X(t)=n) show that p_{n}(t) satisfy the equation p'_{n}=(n-1)p_{n-1}(t)-np_{n}(t) for all n\geq1 How do i work out what is p_{n}(t)=P(X(t)=n) in terms of exponentials. Can you help please? thanks
  7. H

    Birth and Death Process

    Each individual in a biological population is assumed to give birth at an exponential rate lambda, and to die at an exponential rate mu. In addition, there is an exponential rate of increase theta due to immigration. However, immigration is not allowed when the population is size N or larger...
  8. K

    Birth and Death Process

    Let {X(t):t≥0} be a pure Birth process with birth rate λj>0. If X(0)=0, calculate the time it takes to reach a population size of N If we are dealing with a Birth and Death process with X(0)=1, and rates λn=λ, μn=nμ, show X(t)→Poisson(λ/μ).
  9. C

    Birth Process/Poisson Process

    An Island is initially uninhabitated. Creatures arrive as a poisson process of rate a per month. Once there each creature produces offspring as a poisson process of rate b per month. Assume that the Poisson process for arrivals and births are all independent. Assume also that there are no deaths...
  10. A

    Calculate my exact birth date?

    Alright. Say I was born 7:00 A.M. on April 18th, 1990. April 18th, 2009 just passed and I was wondering if all the leap year/days and daylight/savings times were accounted for, when would my birthday be this year? Here's a chart for daylight savings times up to 2015: Saving Time, Saving Energy...
  11. R

    Need help on birth process ?

    How do i do Q1, from this sheet ? I can't find any good links with infomation on birth process. What is the general formula for birth process.