Thoughts - Ambarish

09 Sep 2021

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