Term
| Describe the Bernoulli distribution and giev an example of when the Bernoulli distribution would be used? |
|
Definition
A bernoulli distributed random variable only has two possible outcomes (success or failure).
Bernoulli distributed random variables are commonly used for assessing whether or not a company will default during a specified time period. |
|
|
Term
| How does the binomial distribution work? |
|
Definition
| it evaluates a random variable with two possible outcomes over a series of n trials. The probability of success is constant for each trial and the trials are independent of each other. |
|
|
Term
| Whats the formula for the binomial probability function? |
|
Definition
p(x) = P(X=x) = (number of ways to choose x from n) px (1-p)n-x
Where:
p = the probability of ' success' on each trial (don't confuse it with p(x).
(number of ways to choose x from n): n! / [(n-x)! x!)
|
|
|
Term
| Whats the expected value of a binomial distribution? |
|
Definition
For a given series of n trials, the expected number of successes is given by:
E(X) = np
The variance is given by:
Var(x) = np(1-p) |
|
|
Term
| The poisson distribution... describe it: |
|
Definition
- a discrete probability function
- used for, eg, the number of defects per batch
Poisson random variable X = number of successes per unit
parameter lambda (upside down Y) refers to the average or expected number of succeses per unit.
|
|
|
Term
| Whats the Poisson distribution formula? |
|
Definition
P(X=x) = lambdax e-lambda / x!
|
|
|
