Binomial Distribu�on
A binomial random variable is the number of successes x in n repeated trials of a binomial
experiment. The probability distribu�on of a binomial random variable is called a binomial
distribu�on.
Suppose we flip a coin two �mes and count the number of heads (successes). The binomial
random variable is the number of heads, which can take on values of 0, 1, or 2. The binomial
distribu�on is presented below.
Number of heads Probability
0 0.25
1 0.50
2 0.25
The binomial distribu�on has the following proper�es:
The mean of the distribu�on (μx) is equal to n * P .
The variance (σ2x) is n * P * ( 1 - P ).
The standard devia�on (σx) is sqrt[ n * P * ( 1 - P ) ].
