Binomial random variable
Binomial random variable
The binomial random variable is a discrete random variable that is used to model the outcome from a set of $n$ identical experiments that have one of two possible outcomes which are often referred to as sucess and failure. The Binomial random variable tells you the number of sucessful experiments that were performed. The probability mass function for the Binomial random variable is given by: $$ f(X=x) = P(X=x) = \binom{n}{x} p^{x} (1-p)^{n-x} $$ The expectation for this variable is $\mathbb{E}(X)=np$ and the variance is $\textrm{var}(X) = np(1-p)$.
Syllabus Aims
- You should be able to explain what types of phenomena can be modelled using the binomial random variable.
- You should be able to write out the probability mass function for the Binomial random variable and explain how this expression is derived by using a tree diagram.
- You should be able to calculate the elements of the probability distribution function for the Binomial random variable from the probability mass function.
- You should be able to show that the probability mass function for the binomial random variable is properly normalised.
- You should be able to derive the moment generating functions for the binomial random variable and hence obtain the expectation and variances for this random variable.
Description and link | Module | Author | ||
| A video explaining the derivation of the binomial random variable | SOR3012 | G. Tribello |
Description and link | Module | Author | ||
| Problems involving the binomial random variable | SOR3012 | G. Tribello |
Description and link | Module | Author | ||
| Writing a short project on binomial random variables that includes some small programming components. | SOR3012 | G. Tribello |
Contact Details
School of Mathematics and Physics,
Queen's University Belfast,
Belfast,
BT7 1NN
Email: g.tribello@qub.ac.uk
Website: mywebsite