You are waiting for a time of something to occur
Examples include:
- In some board games, you cannot move forward until you roll a specific number. and that could take several tries.
- Manufacturers of products like switches, relays and hard drives need to know how many operations their products can perform before failing. The critical quantity in this situation is called the waiting time or waiting period. the number of trials before a specific outcome.
Binomial similarities
A geometric distribution has a specified number of independant trials with 2 possible outcomes following Bernoulli Trials. SAME AS BINOMIAL
Binomial Differences
In a geometric distribution, the random variable is number of failures before the sucess occurs In a binomial distribution, the random variable is number of trials
Probability distribution formula
P(x) = q^x * p
p = probability of success. q = probability of failure x - random variable for number of failures before success occurs. usually its success - 1.
Expectation formula
E(x) = = q/p
Example
Calculate the probability distribution for getting out of jail in MONOPOLY in x rolls of dice. p = 6/36 = 1/6 q = 5/6 E(x) = (5/6)/(1/6) = 5 5 tries before getting a success
Geometric Distribution
Why is it called geometric distribution? Lets to an example
Example
p = 0.1 q = 0.9
| x | P(x) |
|---|---|
| 0 | 0.9^0 * 0.1 |
| 1 | 0.9^1 * 0.1 = 0.09 |
| 2 | 0.9^2 * 0.1 = 0.081 |
| 3 | 0.9^3 * 0.1 = 0.0729 |
These numbers are a sequence literally