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

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:

Step-by-step 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:"

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

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:

The mean is the average value of numbers given in the series

The median is the middle value of the given series

The mode is the number that is appears more than any other number given in the series

Step-by-step explanation:

The given series is 31,1,27,23,15,27,25,18,22 (totally 9 numbers)

let us change them in a ascending order like 1,15,18,22,23,25,27,27,31

Mean = 21

Median = middle value of the series 1,15,18,22,23,25,27,27,31

23 is the median

Mode = 27 ( it appears in two times 1,15,18,22,23,25,27,27,31)

final answer is

Mean = 21

Median = 23 and

Mode = 27