CBSE Class 12-science Answered

Binomial Distribution

A binomial random variable is the number of successes x in n repeated trials of a binomial experiment. The probability distribution of a binomial random variable is called a binomial distribution (also known as a Bernoulli distribution).

Suppose we flip a coin two times 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 distribution is presented below.

The binomial distribution has the following properties:

The mean of the distribution (μ_x) is equal to n * p .

The variance (σ²_x) is n * p * ( 1 - p ).

The standard deviation (σ_x) is sqrt[ n * p * ( 1 - p ) ].