Probability Distributions
Probability distribution is also known as Probability function.
- This gives the probabilities of all possible outcomes
- A mathematical function which maps each possible outcome x to the probability p(x)
- The probabilities must all sum or integrate to 1
Discrete and Continous Probability distribution
Discrete probability functions can take only discrete values. Examples include Dead/ Alive , numbers obtained by rolling a die, treatment / placebo, whole numbers
Continuous probability functions can take any value within a range. Examples include blood pressure,weight,the speed of a car.
Probablity mass function
is a function that gives the probability of a discrete random variable which is exactly equal to some value. The following table shows the probablity mass function of roll of a die
| # | x | p |
|---|---|---|
| 1 | 1 | p(x=1) = 1/6 |
| 2 | 2 | p(x=2) = 1/6 |
| 3 | 3 | p(x=3) = 1/6 |
| 4 | 4 | p(x=4) = 1/6 |
| 5 | 5 | p(x=5) = 1/6 |
| 6 | 6 | p(x=6) = 1/6 |
Cumulative distribution function
is a function that gives the probability of a random variable is within some range. The following table shows the cumulative distribution function of roll of a die
| # | x | p(x<=A) |
|---|---|---|
| 1 | 1 | p(x<=1) = 1/6 |
| 2 | 2 | p(x<=2) = 2/6 |
| 3 | 3 | p(x<=3) = 3/6 |
| 4 | 4 | p(x<=4) = 4/6 |
| 5 | 5 | p(x<=5) = 5/6 |
| 6 | 6 | p(x<=6) = 6/6 |