Question

A coin is rigged so that the probability of tossing a head is 0.61. The coin is tossed until the first time that a head turns up. Let T record the number of tosses/trials up to and including the first head. What is the probability distribution of T

Answer 1

For this case the probability of getting a head is p=0.61

And the experiment is "The coin is tossed until the first time that a head turns up"

And we define the variable T="The record the number of tosses/trials up to and including the first head"

So then the best distribution is the Geometric distribution given by:

`T \sim Geo (1-p=1-0.61)`

Explanation:

Previous concepts

The geometric distribution represents "the number of failures before you get a success in a series of Bernoulli trials. This discrete probability distribution is represented by the probability density function:"

`P(X=x)=(1-p)^(x-1) p`

Let X the random variable that measures the number os trials until the first success, we know that X follows this distribution:

`X\sim Geo (1-p)`

Solution to the problem

For this case the probability of getting a head is p=0.61

And the experiment is "The coin is tossed until the first time that a head turns up"

And we define the variable T="The record the number of tosses/trials up to and including the first head"

So then the best distribution is the Geometric distribution given by:

`T \sim Geo (1-p=1-0.61)`