CT4 April 2009 Question 8

[Jia Syuen]

Hi there,

For question b)
mu_{ij}=\frac{i(10-i)}{90}\mu for j=i+1, i=1,2,...9

May I know where the '90' comes from? Thanks in advance.

 

[Andrew Martin]

Hi Jia

The number of possible pairings that could result in a new infection is i * (10 - i). The total number of possible pairings is 10C2 = 45. When a pairing occurs that could result in a new infection, a new infection only occurs 50% of the time. So we have that the probability of a new infection is given by: i * (10-i) / 45 * 0.5 = i * (10-i) / 90.

Hope this helps!