Tuesday, February 12, 2008


I’m not sure if this scribe will be much help but it’ll mostly be based on the question we had for homework last night that we also went over in class.
Enjoy =).

So the question that was given to us in class was:

The annual Oxford - Cambridge boat race, has been rowed regularly since 1839. Using data from 1839 up to 1982, there were 57 Oxford wins and 67 Cambridge wins. If the relationship between the results of a given year and the results of the previous year are considered, the following table can be constructed:
--This means that during the 57 games Oxford played, they won 35 times and lost 22 times.
Giving us: 35 + 22 = 57
--Also during the 67 games Cambridge played, they won 23 times and lost 44 times.
Giving us: 23 + 44 = 67

Then part A of the question asked us to “convert the ‘number of wins’ to percentages."
To calculate the number of wins, you divide:

Once you calculated the wins, you also have to convert the number of loses to percentages and to get that, you divide:

After all the calculations are done, we place the numbers back into the matrix and we end up with a transition matrix that looks like this:

Now moving onto part B of the question, which is asking us to find the probability that oxford will win a game this year and the second and third year.

In order to find the probability that Oxford will win this year and the following years, we must construct a state matrix that looks like this:
--The “1” in this state matrix represents the probability that oxford will win.
--The “0” represents the probability Cambridge won't win.

Now that we have both the state matrix and the transition matrix, we can use multiplication to solve part B of the question.

Before I go onto part C, I’ll do part D of the question first because it’s exactly the same as part B. The only difference is that state matrix because now, it looks like this:--This state matrix is different from the previous one we had earlier because now we’re trying to look for the probability Cambridge will win instead of Oxford. Which is why the zero and the one have switched sides.

Now that we have all the information we need, repeat exactly what we did in Part B to part D. Giving us:

Now going back to part C, the question is asking us “over many years, what percentage of games will Oxford win and Cambridge?”

Since the question isn’t asking for when it stabilizes, I just picked a random number like 50, and multiplied it, like so:
And since the question isn’t asking to prove if these are stabilized, I didn’t multiply again by 51 and just left it as is.

Anyways I guess this is the end of my scribe and hopefully it might be some help to some of you. And for tomorrow's scribe, it’ll be ickie

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