Harvard statistics 110, video 8 note(random variables & their distribution

8:56 2014-10-07 Tuesday

start Harvard statistics, video 8

random variables & their distribution


8:57 2014-10-07
Bernoulli(p) => Binomial(n,p)


8:58 2014-10-07
Binomial distribution


8:58 2014-10-07
X ~ Bin(n, p)


story: X is the #successes of n independent Bernoulli(p) trials


9:01 2014-10-07
indicator r.v.


9:02 2014-10-07
sum of random indicator variables:


X = X1 + X2 + ... + Xn


9:03 2014-10-07
i.i.d. == independent identically distributed


9:05 2014-10-07
confuse r.v. with distribution


9:06 2014-10-07
event is a subset of sample space


9:23 2014-10-07
event is a subset of outcomes


9:24 2014-10-07
CDF == Cumulative Distribution Function


9:25 2014-10-07
CDF is a way to describe the distribution.


9:46 2014-10-07
PMF is only for discrete r.v.


9:47 2014-10-07
continuous r.v.


9:48 2014-10-07
the reason we use CDF is that it's more general.


PMF is only for discrete r.v.s


9:53 2014-10-07
those are equally valid ways to describe the distribution.


9:53 2014-10-07
that's why it's called Binomial distribution,


because it's connected to the binomial theorem.


9:55 2014-10-07
X ~ Bin(n, p), Y ~ Bin(m, p) => X+Y ~ Bin(m+n, p)


9:59 2014-10-07
mathematically we're adding 2 functions


9:59 2014-10-07
P(X + Y = k) // in statistics, this is called convolution


10:06 2014-10-07
where we condition on X, and using the LOTP(Law Of Total Probability)


10:07 2014-10-07
independence mean we can just cross this, thus


P(A|B) = P(A)


10:10 2014-10-07
the key assumption is that the trials


are indepent & they all have the same probability of success.


10:15 2014-10-07
hypergeometric distribution