Geometric Distribution: Overview, Questions, Preparation

In a progression of preliminaries, if you expect that the probability of one or the other achievement or disappointment of an irregular variable in every preliminary is the equivalent, geometric distribution gives the probability of making progress after N number of disappointments. The appropriation is a bunch of probabilities that presents the opportunity of progress after zero disappointments, one disappointment, two disappointments, etc.

Definition:

A mathematical appropriation is characterised as a discrete probability circulation of an arbitrary variable "x", which fulfils a portion of the conditions. The mathematical circulation conditions are:

A wonder that has a progression of preliminaries 

Every preliminary has just two possible results – either achievement or disappointment. 

The probability of progress is the equivalent for every preliminary.

Formula:

In probability and insights, mathematical dispersion characterises the probability that the first achievement happens after the preliminaries' k number. On the off chance that p is the probability of progress or disappointment of every preliminary, at that point, the probability that achievement happens on the kth preliminary is given by the formula.

Pr(X=k)=(1−p)k−1p

Example:

Consider a couple who plans to have a child and will continue to have babies until it is a girl. What is the probability they have zero boys, a boy and two boys and so on until a girl is born?
A person is looking for new jobs that are both difficult and fulfilling. What is the probability that he will leave zero times, once, twice, or so until he finds his ideal job?
A pharmaceutical company will conceive of a new drug to treat a certain disease that will have minimal side-effects. What is the likelihood that zero drugs fail to test, a medicine fails to test, two drugs fail to test and so on until they have designed the ideal medicine?

In class 12: In the chapter Probability, various vital theorems and concepts have been discussed with the definitions and formula(s) and the questions on it. The chapter has a weightage of 8 marks.

1. Find the probability that Stéphane wins seven games if he plays ten games.
Solution. Total game played having a Binomial, n = 10, p = 0.60. P( X = 7 ), defines the probability
= 10C7 ⋅ 0.60 7 ⋅ 0.403 ≈ 0.21499, will be the probability of the game.

2. The mean and Variance of geometric distribution are:
Solution. The mean is in the form of  q/p and variance can be represented as q/p2

3. Which of the following is asymmetrical distribution?
Solution. "T" in variable form will be in asymmetrical distribution

Q: How can we apply geometric distribution in statistics?

Q: Define geometric distribution

Q: Give the mean and Variance of the geometric distribution.

Q: Give the characteristics of the geometric distribution.

Q: What is the difference between a binomial and geometric distribution?