📗 -> 10/15:
🎤 Vocab
❗ Unit and Larger Context
Small summary
✒️ -> Scratch Notes
Geometric Parameter
Probability p of a success
Keep going until there is a success
p - Win
(1-p) - Lose
Winning for the first time on the 4th try:
- Actually just lose-lose-lose-win
- (1-p)^3 (p)
PMF - Probability Mass Function.
a)
What is the pro that it takes 4 transmissions to receive the message?
p=0.2
Indicator
x={0,1}
different from geometric, since an indicator is a one trial thing. Geometric could theoretically go on forever
Binomial
Play n games and win k times
General PMF:
Proof by seperating expectation of each trial out
^ n trials, each having a probability p of occurring
Have 5 tries, how likely to win twice? p=0.3
You can win in multiple different orders
A common question will be probability of winning or losing more than a certain value. Use set compliment rules to facilitate this:
Probability that I win two or more times, out of 45 games with probability p?
Uniform:
Every int is equally likely from
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