These notes offer a focused overview of the Binomial and Poisson Distributions, two fundamental probability distributions used in statistical analysis.
Binomial Distribution:
Definition: The Binomial Distribution models the number of successes in a fixed number of independent trials, each wit...
Binomial Distribution
Bernoulli Distribution: A random variable X which takes two values 0 and 1
with probabilities q and p is called Bernoulli variate and P(x=1) = p and
P(x=0) = q, q = 1−p, is said to be a Bernoulli Distribution, where p and q take
the probabilities for success and failure respectively.
Tossing a coin and considering heads as success and tails as failure.
Consider the following type of random experiment:
1. The experiment consists of n repeated Bernoulli trials –
each trial has only two possible outcomes labelled as success and failure;
2. The trials are independent - the outcome of any trial has no effect on the
probability of the others;
3. The probability of success in each trial is constant which we denote by p.
,
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