STA1000S Notes
Module 1 – Probability ................................................................................................................... 2
Module 2 – Exploring Data.......................................................................................................... 20
Module 3 – Random Variables ................................................................................................... 28
Module 4 – Probability Distributions ....................................................................................... 35
Module 5 – Hypothesis Testing ................................................................................................. 56
,Module 1 – Probability
Week 1:
Probability Versus Odds
Probability reflects the number of ways of getting specific outcome relative to the
total number of ways of conducting the experiment.
Odds reflect the number of ways that give you the event of interest relative to the
number of ways that don’t give you the event of interest.
Statistical Distributions
Statistical distributions are long-run patterns of various outcomes – used to predict
etc.
Excel Formulas
= rand()
→ Generates a random number between 0 and 1. By pressing F9, random numbers
are re-generated.
= countif (A1:A20;1)
→ “A1:A20” refers to range of data.
→ “1” refers to what you’re looking for.
By pressing F4, you lock the data set to specific numbers.
Fair Game
• Nobody is expected to win and nobody is expected to lose in the long run.
Example:
I have a stall where people come and bet on the numbers from die throws. Each bet
is R1. If Amy bets R1 on all 6 numbers, in order for it to be a fair game, she should
win R6 if she’s correct – what she pays = what she wins.
,Win Percentage
• Indicates the percentage of what we have received in the form of bets that
we pay back in winnings.
• The amount we pay back of what we take in.
Example:
Fair payout must be
reciprocal of prob of win
3/7 → 2 1/3
House Advantage
Main criteria:
• House maintains a portion of pay-out for the winning number.
o This = the amount we [the stall owners] retain.
Example:
For a winning number the payback would be R5.50. The 50c goes to the house
(house advantage). The payback is less than the outlay of the player.
, Example:
Expected Gain/Loss
Example:
NOTE: If E(G or L) < 1, then it’s a loss!
Module 1 – Probability ................................................................................................................... 2
Module 2 – Exploring Data.......................................................................................................... 20
Module 3 – Random Variables ................................................................................................... 28
Module 4 – Probability Distributions ....................................................................................... 35
Module 5 – Hypothesis Testing ................................................................................................. 56
,Module 1 – Probability
Week 1:
Probability Versus Odds
Probability reflects the number of ways of getting specific outcome relative to the
total number of ways of conducting the experiment.
Odds reflect the number of ways that give you the event of interest relative to the
number of ways that don’t give you the event of interest.
Statistical Distributions
Statistical distributions are long-run patterns of various outcomes – used to predict
etc.
Excel Formulas
= rand()
→ Generates a random number between 0 and 1. By pressing F9, random numbers
are re-generated.
= countif (A1:A20;1)
→ “A1:A20” refers to range of data.
→ “1” refers to what you’re looking for.
By pressing F4, you lock the data set to specific numbers.
Fair Game
• Nobody is expected to win and nobody is expected to lose in the long run.
Example:
I have a stall where people come and bet on the numbers from die throws. Each bet
is R1. If Amy bets R1 on all 6 numbers, in order for it to be a fair game, she should
win R6 if she’s correct – what she pays = what she wins.
,Win Percentage
• Indicates the percentage of what we have received in the form of bets that
we pay back in winnings.
• The amount we pay back of what we take in.
Example:
Fair payout must be
reciprocal of prob of win
3/7 → 2 1/3
House Advantage
Main criteria:
• House maintains a portion of pay-out for the winning number.
o This = the amount we [the stall owners] retain.
Example:
For a winning number the payback would be R5.50. The 50c goes to the house
(house advantage). The payback is less than the outlay of the player.
, Example:
Expected Gain/Loss
Example:
NOTE: If E(G or L) < 1, then it’s a loss!
