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Bernoulli Distribution
The Bernoulli distribution is one of the simplest discrete probability distributions. It describes events that have
exactly two outcomes. Let us take the example of tossing an impartial coin. Either Head or Tail will appear. The
result will only be 0 (failure) or 1 (success) if we prioritise one of them above the other (success). An impartial coin
has a probability of 0.5 for each outcome. Always assume a binary outcome: true or false, head or tail, success or
failure, etc.
The probability mass function or PMF of Bernoulli Distribution is given as
P(n) = pn ×(1–p) 1–n
The expected value of the distribution can be derived by taking a weighted average of possible outcomes:
E(x) = p × 1 + (1–p) × 0
The following graph shows the Bernoulli distribution:
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S s s e c c u e r u l i a F
Binomial Distribution
A Binomial distribution is a common probability distribution that models the probability of obtaining one of two
outcomes under a given number of parameters. It totals the number of trials when each trial has an equal chance
of producing a particular result. By dividing the quantity of independent trials by the number of successful trials,
one can calculate the value of a binomial. For the trials we are looking at, the probability of receiving a success in
a binomial distribution must stay constant. Since there are only two possible outcomes when tossing a coin, for
instance, the probability of flipping a coin is 1/2 or 0.5 for each experiment we conduct.
There are four different criteria of binomial distributions described below which the binomial distributions need to
fulfil. These are as follows:
1. The number of the trials or the experiments must be fixed. As you can only figure out the probable chance of
occurrence of success in a trial you should have a finite number of trials.
2. Every trial is independent. None of your trials should affect the possibility of the next trial.
3. The probability always stays the same and equal. The probability of success may be equal for more than
one trial.
4. There are only two mutually exclusive outcomes, i.e., success or failure.
Distributions in Data Science 141

