I'm having a bit of a problem proving the second condition for a martingale, the discrete time branching process Z(n)=X(n)/m^n, where m is the mean number of offspring per individual and X(n) is the size of the nth generation.
I have E[z(n)]=E[x(n)]/m^n=m^n/m^n (from definition E[X^n]=m^n) =...
For the probability of the number of infective's increasing in one time step, I found the answer is:
∆tβi(N-i)/N
where β is the contact rate, ∆t is the time step, i is number of infectives,N is total number of susceptible's and infective's
I can't quite see where this is coming from. β is...
I'm having a little trouble understanding the mean hitting time of a random walk, with p(i,j) = p if j=i+1, q if j=i-1 and 0 otherwise. 0 is an absorbing state and no upper absorbing state ie. dealer has unlimited amount of money.
Need to work out the mean hitting times k(i)(0) for i=0,1,2...
I can't seem to wrap my head around the types of sums used in probability theory, and here is a classic example. Section 6.1 of this article:
http://en.wikipedia.org/wiki/Expected_value#Discrete_distribution_taking_only_non-negative_integer_values
The first line of the proof, what is going...
Ok, so if I move a proton to the mid point between 2 point charges -10 and +6 it will gain energy from the force it had to use to move against the positive charge, but it will lose even more evergy than this from the negative charge attracting it? Hence the electric potential energy and voltage...
I'm having trouble fully understanding what electrical potential means. If there are two point charges of opposite signs and a point charge somewhere around them, we simply add the two voltages separately? Not as a vector sum?
Also the concept of negative potential, does this mean that the...
Hi this is my first time posting on here so hopefully I get it right.
Given the linear system x'(t) = Ax(t)' with an eigenvalue (lambda) of algebraic multiplicity 2 and geometric multiplicity 1 (repeated root), one solution is w.exp(lambda t) and the other w.t.exp(lambda t) + u.exp(lambda t)...