1. Random Variable
Random Variable – Numerical Result Determined by the Outcome
of a Probability Experiment.
Ex1: Roll a Die X = # of Spots
X |
P(X) | 1/6 1/ / / / /6
Ex2: Toss a Coin Twice X = # of Heads
X |
P(X) | ¼ ½ ¼

2. Ex3: Inspect an Item X = Diameter
Ex4: Select and Employee X = Tenure with Company
Probability = The Area of the Random Variable Distribution Curve

3. Discrete Random Variable – Takes on Only Integer Values
Continuous Random Variable – Takes on All Real Values Over a Range
Measures for Random Variables
Mean µ = E(X) = ∑ X•P(X) Expected Value
2 Coin Toss:
X |
P(X) | ¼ ½ ¼

4. 3 Coin Toss:
X |
P(X) | / / / /8
Variance of a Random Variable
σ2 = V(X) = ∑ (X - µ )2•P(X) Variance
σ2 = E(X2) - µ Shortcut Formula

5. 2 Coin Toss:
X |
P(X) | ¼ ½ ¼
(X-µ) |
(X-µ) |
(X-µ)2•P(X) |
3 Coin Toss:
X |
P(X) | / / / /8
(X-µ) |
(X-µ) |
(X-µ)2•P(X) |

6. Example: Insurance Claim X = $ Loss
$ Loss P(X) X•P(X) (X-µ) (X-µ ) (X-µ )2•P(X) 2,
10,
50,

7. St Petersburg Paradox: Gambling Game in which you toss a coin until you get a Tail.
# Tosses |
Payoff | $ $ $ $ $ $ $ $256 $512
P(X) | ½ ¼ / / / / / / /512
Expected
Payoff =
Tosses =