Geometric Distribution

Geometric Distribution:

Repeat Bernoulli trail infinite times(because we do not know how many times to repeat it)

Experiment: Tossing fair coin.

Interested in: The number of tosses until we see the first head.

Random number= {1,2,3.....infinite}

Geometric distribution is useful in any situation involving "waiting time".

i.e.)continuously doing a trial & want to know that after certain time will get success.

Assumption:

• Independent trial (success/failure in one trail does not affect the outcome of other trails)
• Identical (Probability of success 'p' in each trail is same)

SITUATION:

Hawker selling belts outside a subway station, what is the chance that the first belt will be sold after 5th person passes by?

[i.e.)first 4 trail - Failure, 5th trail - Success]

=>(1-p)*(1-p)*(1-p)*(1-p)*p

=>(1-p)^4*p

Probability mass distribution of geometric random variable px(x) -> fully specify in terms parameter "p".

where p be the probability of success.

In general geometric distribution formulae:

(1-p)^(x-1)*p

Geometric distribution falls Left to Right always irrespective of "p"

consider 25 random values:

if p=0.2

if p=0.5 if p=0.9