Discrete Probability Distributions

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Probability Mass Function (p.m.f, Discrete Probability Density Function)

Definition

The p.m.f. of a discrete random variable is defined as

Intuition

The p.m.f. is literally just the probability function of any discrete outcome of an experiment

Example

Sum of two dice roles:

X
2
3
12
Properties

Suppose is an random variable with p.m.f. , then

Example

A random bridge hand is dealt.
number of aces

X f
0
1
2
3
4

(see choose)

Example

Suppose has a p.m.f . Find the p.m.f. of . Is it ?

X f
-1
0
1

p.m.f for :

?
0
1

It's not ,

Example

Suppose we toss a coin twice.

  • number of heads
  • number of tails
0
1
2
0
1
2

Same p.m.f. is ok.