STAT371 DISCUSSION 4 September 29, 2002
TA: Ruiyan Luo
Office: 4268 CSSC
Office hours: TW 2:30–3:30pm
Phone number: 262-8182
E-mail: [email protected]
1. Bionomial distribution
•Four conditions for a binomial random varialbe:
–Binary outcomes: there are two possible outcomes for each
trial (success and failure)
–Independent rials: the outcomes of the trials are independent
of each other
–n is fixed: the number of trials, n, is fixed in advance
–Same value of p: the probability of a success on a single trial
is the same for all trials
•The binomial distribution formula
For a binomial random variable, the probability that the ntrials
result in jsuccesses (and n−jfailures) is given by the following
formula:
P r{jsuccesses}=nCjpj(1 −p)n−j
where nCj=n!
j!(n−j)! and x! = x(x−1)(x−2)...(2)(1), 0! = 1.
nCjhas some properties:
nC0=nCn= 1
nCj=nCn−j
•Properties of binomial distribution:
–expectation (or mean) of X is np.
–variance is np(1 −p); standard deviation is qnp(1 −p)
–the binomial distribution is symmetric if and only if p= 0.5
1
