Question

1. Imagine a coin toss experiment, where P(Heads)-P(Tails) 0.5. Define a random variable of your choice for this experiment and come up formulation for a question about this experiment, so that The distribution of a random variable for this experiment follows a binomial distribution The distribution of a random variable for this experiment follows a geometric distribution a. b. Note: you are only required to come up with the problem statement. Note, that this experiment itself is a Bernoulli trial. Binomial and geometric distributions are an extension of n Bernoulli trials.

Answer 1

Solution:

we are given that: P(Head) = P(Tail) = 0.5

Define Success as Getting Head, that is: X = Getting Head , then X follows Bernoulli distribution with parameter p = 0.5

Part a) we have to define a random variable which follows a Binomial distribution.

Binomial distribution is extension of Bernoulli distribution which includes n Bernoulli trials with constant probability of success rate p.

           Suppose coin is tossed n times, then random variable X = Number of heads occurred in n Bernoulli trials follows Binomial distribution with parameters n trials and p = probability of success = 0.5

Part b) we have to define a random variable which follows Geometric distribution.

Geometric distribution : In geometric distribution , a random variable X is Number of failures before first success with probability of success = p and probability of failure = q.

Thus toss a coin until we get first Head , then X = Number of tails before first Head follows Geometric distribution with parameter = p = 0.5