S2

Monday 17th September

POISSON

What's it's all about! The formula book gives the formula for P(X = r) and all the cumulative frequencies. Remember that we need:

Events to be random and independent The 'average' occurrence to be fixed and known (lambda)

The lesson:

Today we saw how Poisson is a very good approximation for the Binomial distribution so long as: (i) n is large (ii) p is small (iii) np is fairly small (no larger than 10)
 * 21st** **September**

We explored why this is the case - it's all to do with the 'infinite expansion of e x - something we'll explore later in the Further Pure course.

The lesson will appear here: Homework set for next Friday - FP1, Jan 2005 No lesson with me before Friday - get on with that paper or some STEP stuff.

This was the first lesson on the NORMAL distribution. We learned that... (i) the normal distribution is a CONTINUOUS distribution (ii) the two parameters are the MEAN and the VARIANCE (the standard deviation is the square root of the variance). A normal variable will be defined an N(mean, variance) (iii) Approximately 68% of the 'population' is located within 1sd of the mean, 95% within 2sds and 99.8% within 3sds. We can use the Normal tables in the formula book to solve problems (two tables, working in 'opposite directions')
 * Friday 28th Sep**

Here's the lesson:

We looked a bit more at the Normal distribution - specifically solving problems where we have to find the mean and/or the standard deviation. We also started looking at how the Normal distribution can work as an approximation to the Binomial distribution, so long as n is large, p is not too close to 0 or 1 and we remember our CONTINUITY correction - we'll discuss this more over the next few lessons.
 * Monday 1st October**

Here's today's lesson: