Question

3. (a) Define a Bernoulli process and random and describe a Bernoulli random variable.

(b) Find the means and Variance of a Bernoulli random variable.

(c) Define a binomial process and random variable and describe a binomial random variable

Answer 1

a) A Bernouilli distribution is a discrete probability distribution for a Bernouilli trial — a random experiment that has only two outcomes (usually called a “Success” or a “Failure”). For example, the probability of getting a heads (a “success”) while flipping a coin is 0.5. The probability of “failure” is 1 – P (1 minus the probability of success, which also equals 0.5 for a coin toss). It is a special case of the binomial distribution for n = 1. In other words, it is a binomial distribution with a single trial (e.g. a single coin toss).

The probability density function (pdf) for this distribution is p^x (1 – p)^1-x,

C) A binomial variable with n trials, represents the number of successes out of n trials. Abinomial variable with n trials can be thought of as the sum of n independent Bernoulli variables, each with the same success probability as the binomial variable.

b)