rsq_a
Mar15-10, 04:56 PM
Suppose that each bacterium in a colony splits into two identical bacteria after an exponential time with parameter \lambda, which then split independently in the same way. Let X_t be the size of the colony at time t and suppose X_0 = 1.
Why would it makes sense (intuitively) that
P(X_t = n) = (1-e^{-\lambda t})^{n-1} e^{-\lambda t}?
I proved it as part of the question, but I'm unable to find a simple explanation why the formula makes sense.
Why would it makes sense (intuitively) that
P(X_t = n) = (1-e^{-\lambda t})^{n-1} e^{-\lambda t}?
I proved it as part of the question, but I'm unable to find a simple explanation why the formula makes sense.