Recent content by Absolut

Ok, thanks for the advice. Any ideas on what formulas I should be using?

Homework Statement A repairman fixes broken televisions. The repair time is exponentially distributed with a mean of 20 minutes. Broken television sets arrive at his shop according to a Poisson process with arrival rate 12 sets per working day. (8 hours). (i) What is the fraction of time that...

The multiplication by 2 was "accidental", I got mixed up with another similar question I was doing.

I've been trying to do the calculations in my head, so it's a little tricky for me to get the matrix straight...

\left(\begin{array}{cccc}0&0.5&1.0&0\\0.85&0&0&0\\0&0.8&0&0\\0&0&0.5&0\end{array}\right) * \left(\begin{array}{cc}3\\2\\2\\0\end{array}\right) = P(1) \left(\begin{array}{cccc}0&0.5&1.0&0\\0.85&0&0&0\\0&0.8&0&0\\0&0&0.5&0\end{array}\right) * P(1) = P(2)...

Well, I'm trying to find a value for A(P(t)) - A is the matrix that I found at the very begining, so I was thinking I should be subbing in the birth and death rates into that matrix to find P(t)/P(t+1)?

P(t+1) = AP(t) P(t+1) = \left(\begin{array}{cccc}o&b_1&b_2&0\\1-d_0&0&0&0\\0&1-d_1&0&0\\0&0&1-d_2&0\end{array}\right) * P(t)

I'd imagine I start off by subbing the values into the given matrix: \ P = \left(\begin{array}{cc}P_0 \\P_1\\P_2\\P_3\end{array}\right) = \left(\begin{array}{cc}3\\2\\2\\0\end{arra y}\right) I also have P(t + 1) = AP(t). So maybe sub in values for t = 0, 1 and 2 (but sub them into...

That's actually part of the next question, which I've only just seen: Consider the evolution of the species over the next three years, where the initial population is P_0 = 3, P_1 = 2, P_2 = 2, P_3 = 0. Using the following birth and death rates: d_0 = 0.15, b_1 = 0.5, d_1 = 0.2 b_2 =...

My head is fried... sorry for all the obvious questions! f(1) is negative, f(2) is positive... so somewhere in between there is an f(x) that is equal to zero. I was concentrating on the magnitude instead of the signs! Thanks for your help.

f(2) is 12.94...

I only spotted my mistake when I took the time to type it all out in latex code - and it was a small mistake with mixing up a zero in a place where it shouldn't have been! So I did manage to get out my eigenvalue equation, but now I am stuck on another section: If d_0 = 0.15, d_1 = 0.2, d_2...

Ok, so here's my full work on finding the determinant so far: \left(\begin{array}{cccc}-\lambda&b_1&b_2&0\\1-d_0&-\lambda&0&0\\0&1-d_1&-\lambda&0\\0&0&1-d_2&-\lambda\end{array}\right) -\lambda \left(\begin{array}{ccc}-\lambda&0&0\\1-d_1&-\lambda&0\\0&1-d_2&-\lambda\end{array}\right)...

Appologies for my poor latex!

\left(\begin{array}{cccc}-\lambda&b_1&b_2&0\\1-d_0&-\lambda&0&0\\0&1-d_1&-\lambda&0\\0&0&1-d_2&-\lambda\end{array}\right) That's the (A-\lambdaI) matrix that I'm using Then I'm trying to find the determinant by taking each element of the first row as follows: -\lambda...