The binomial distribution Flashcards
1
Q
random variable
A
a variable whose value is a numerical outcome of a random phenomenon. Usually a capital letter such as X
2
Q
discrete random variable
A
X, takes a finite number of values, denoted by x1…xk
A probability model of X is given by assigning probabilities Pi to these outcomes, P(X=xi) = pi
3
Q
the probability should add to
A
1
4
Q
number of ways of choosing r from n things
A
(n,r) = nCr = n!/r!(n-1)!
5
Q
binomial requirements
A
- fixed number of n observations
- n observations are all independent
- two categories of observations: success of failure
- the probability of success, p, is the same for each observation
6
Q
binomial distribution
A
the distribution of the count X of the successes in the binomial setting is called the binomial distribution and has parameters n and p
7
Q
binomial equation
A
P(X=r) = (nr)p^r(1-p)^n-r where r = 0, 1…n
P(X=r) can be written X~B(n,p)
8
Q
non-binomial settings
A
- not constant
- not independent
9
Q
cdf
A
most number of successes
10
Q
A
exact number of successes
