Bernoulli Distribution with Example
In this class, We discuss Bernoulli Distribution with Example.
The reader should have prior knowledge of probability distributions. Click Here.
Bernoulli Distribution:
Bernoulli distribution is a discrete probability distribution with only two possible outcomes.
One outcome we call success or 1
Another outcome is Failure or 0
Example:
Toss a coin.
The outcomes are head or tail.
Head is considered a success.
Tail is considered a Failure.
Important: Roll a dice is considered as bernoulli distibution.
Outcome 6 is considered a success.
The other outcomes are considered Failure.
Bernoulli probability distribution table:
Toss a coin.
Success = head
The below table shows the probability distribution.
Roll a dice.
success = 6
Failure = 1, 2, 3, 4, 5.
The below table shows the probability distribution.
Bernoulli probability distribution graph
The below diagram shows the probability distribution graph for rolling dice.
On the X-axis, we take 0 and 1.
On the Y-axis, we take the probability values.
If P(success) = p for a bernoulli distribution then P(Failure) = 1-p.
Probability Mass Function for Bernoulli Distribution:
PMF = Px(1-P)1-x
PMF = f(x)
Why the above PMF?
f(0) = 1-P
f(1) = P
Expected value of Bernoulli distribution.
E(X) = all x Σ xf(x)
= 0(1-P) + 1(P)
= P
Variance of Bernoulli Distribution:
Variance = E(X2) - (E(X))2
= P - P2
= P(1-P)
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