Bernoulli distribution is one of the discrete probability distributions which only answers the probability in yes or no. It is described if the event is about to happen so it may have two outcomes, one is yes and other is no. So, probability of a yes happening is denoted by p and probability of no happening is (1-p). We can take an example to understand it more clearly. If we assume that whenever an even number comes we win and odd if we lose. So, for winning p=3/6 = 1/2. And q= (1-p) = (1-1/2) = 1/2, hence this will be the probability for this distribution.
This is the graph showing the probabilities of the distribution. Only two options are available, yes or 1 and no or 0. Here p is the probability for 1 and 1-p for 0.
Formula for Bernoulli distribution is,
f(k;p)=pk+(1-p)(1-k)
Where,
P is the probability, k is the possible number of outcomes, and f is probability mass function.
And,
We can also express this formula as,
The arithmetic mean can also be taken as the weighted average. Below is the formula for the mean of the Bernoulli distribution,
E[X] = p
Variance for Bernoulli distribution can be written as,
Var[X] = p(1-p) = p*q
Applications of Bernoulli Distribution:
- It can be used in the medical field by fetching the data of a single patient and a model can be made on that.
- In logistic regression Bernoulli is used for the outcomes of the dice roll.
- It also has applications in aerospace and engineering.
Data Science Intern at Sophos Knowledge, Student at NMIMS