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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

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Answer:

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)

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