The document discusses random variables and discrete probability distributions, explaining that a random variable's value is determined by a random experiment. It illustrates how to construct a discrete probability distribution, such as the outcomes of flipping three coins or rolling two dice, showing that probabilities sum to one. Examples highlight how to derive probability tables for various random outcomes.

1. Understanding Statistics
Random Variation and Discrete Probability Distribution

2. Random Variation and Discrete Probability Distribution
 Random Variable – Variable whose value is determined by a random experiment:
 Ex: flipping coins, draw cards, observing population
 Discrete Probability Distribution – Table or Formulas that list the probability for each outcome of the random variable, X
 Ex: flip 3 coins at same time .
 - Let random variable X be heads showing
Discrete Probability Distribution
H H H  3Heads
H H T  2Heads
H T H 2Heads
H T T  1Head
T H H  1Head
T H T
T T H - what makes it discrete is that the number of values is finite
T T T - here you can have only 4 columns (outcome) and 4 probabilities
1/8 + 3/8 + 3/8 + 1/8 = 1 – means I cover all possible outcomes
We listed all possible outcome, note there are only one way to get 3 H is 1 and get 0 H is 1 si 3 heads is a very low probability
Discrete Probability Distribution Table
χ 0 1 2 3
P(x=χ) 1/8 3/8 3/8 1/8

3. Random Variation and Discrete Probability Distribution
Problem: what is the Probability Distribution for Random Variable (X) which will be the sum of 2 rolled
dice
Discrete Probability Distribution Table
χ 2 3 4 5 6 7 8 9 10 11 12
P(X=χ) 1/36 2/36 3/36 4/36 5/36 6/36 5/35 4/36 3/36 2/36 1/36
36
36
= 1