Krdytkyu

Chronologies Années : 1804 1805 1806  1807  1808 1809 1810 Décennies : 1770 1780 1790  1800  1810 1820 1830 Siècles : XVIII e  siècle   XIX e  siècle  XX e  siècle Millénaires : I er  millénaire   II e  millénaire  III e  millénaire Chronologies géographiques Afrique Afrique du Sud, Algérie, Angola, Bénin, Botswana, Burkina Faso, Burundi, Cameroun, Cap-Vert, Centrafrique, Comores, République du Congo, République démocratique du Congo, Côte d'Ivoire, Djibouti, Égypte, Érythrée, Éthiopie, Gabon, Gambie, Ghana, Guinée, Guinée-Bissau, Guinée équatoriale, Kenya, Lesotho, Liberia, Libye, Madagascar, Malawi, Mali, Mauritanie, Maurice, Maroc, Mozambique, Namibie, Niger, Nigeria, Ouganda, Rwanda, Sao Tomé-et-Principe, Sénégal, Seychelles, Sierra Leone, Somalie, Soudan, Soudan du Sud, Swaziland, Tanzanie, Tchad, Togo, Tunisie, Zambie et Zimbabwe   Amérique Antigua-et-Barbuda, Argentine, Bahamas, Barbade, Belize, Bolivie, Brésil, Canada (Nouveau-Brunswick...

4 $begingroup$ I encountered this problem while trying out various practice problems to study for my stochastic processes test. (It's not homework, it's just a practice problem). Consider a pure birth process on the states 0,1,...,n for which $lambda_k = (N-k)lambda$ for $k = 0,1,...,N$. Suppose that $X(0) = 0$. Determine $P_n(t) = Pr{X(t)=n}$ for $n = 0,1,2$ The solution that I was given was $P_n(t) = {N choose n}e^{-(N-n)lambda t}(1-e^{-lambda t})^n$. Could someone please explain this problem's solution to me? I can't seem to derive it from any formula that I have been given by the class. Any help would be greatly appreciated! stochastic-processes share | cite | improve this question ...