What content should I revise before doing binomial distributions in ext 1? (1 Viewer)

[Daq]

I was looking through the y11 advanced and ext 1 textbooks (cambridge) to see what probability/combinatorics was necessary to revise from both, and I just do not know what content is necessary to do Binomial Distributions, my upcoming topic for EXT 1.

This is probs my weakest topic, so I want to spend a good amount of time studying for it, but I just don't know where to start. Could anyone who has done the course give me advice on what exactly I should revise from y11 textbooks? I know we need combinatorics (UGGHHH) but I don't know what else.

 

[liamkk112]

probability and combinatorics yeah, but combinatorics only a little bit

binomial distribution you basically need to know these facts:
- X~ Bin(n,p) arises from a situtation where you have n independent Bernoulli (aka true or false, success or failure variables, e.g. flipping a coin and checking the prob that you get heads or tails on that flip) variables each with probability p of success
- , you may like to think of this as "the probability of X having k successes is the same as choosing k of the n independent Bernoulli variables as having a success outcome"
- E(X) = np, Var(X) = np(1-p). the derivations of these are out of syllabus from memory, but i'll at least provide the expectation derivation:
suppose where each is a Bernoulli variable with probability of success p (also they're all independent from each other)
then if we know that the expectation is linear, so

but we know that for which u can easily get from the definition. so
as there are n independent bernoulli variables. the variance is done the exact same way, just using the fact that variance is linear rather than the expectation

that's pretty much it, binomial variables aren't too hard, as long as you know that they arise from bernoulli variables and know properties of bernoulli variables