Mastering Conditional Probability and Markov Models
Conditional Probability
Instead of saying: “The chance of rain given I saw a wet umbrella,” we write it as: P(rain | wet umbrella).
The Difference in One Sentence
| Question | Filter First? | Divide By |
|---|---|---|
| P(ice cream | sunny) | YES, only look at sunny days | Number of sunny days (5) |
| P(sunny AND ice cream) | NO, look at everything | Total days (10) |
Think of It This Way ðŸ§
- AND = out of the whole world.
- GIVEN = out of a smaller filtered world.
So now you know two things:
- P(A | B) = out of only the B days, how many have A (divide
The Great Gatsby: Plot, Characters, and Key Themes
Chapter 1: Nick Carraway & West Egg’s Elite
Nick Carraway: Narrator and newcomer to West Egg; curious, observant, and initially nonjudgmental.
Daisy Buchanan: Nick’s cousin; charming, nostalgic, but emotionally shallow.
Tom Buchanan: Daisy’s wealthy husband; aggressive, arrogant, and unfaithful.
Jordan Baker: Daisy’s friend; cynical, independent, and somewhat dishonest.
Jay Gatsby: Appears only briefly; mysterious neighbor who watches the green light across the bay.
Nick Carraway opens the novel
Read MoreFundamentals of Channel Capacity and Data Coding
Channel Capacity Concepts
Channel capacity is the maximum amount of reliable information that a communication channel can carry, typically expressed in bits per second (bps), with an arbitrarily low probability of error.
There are two primary contexts for channel capacity: one for continuous-time channels and another for discrete-time channels.
Discrete Memoryless Channels
A discrete memoryless channel is defined by:
- An input alphabet X = {x1, x2, …, xn}, which is the set of symbols that can be transmitted
The Great Gatsby: Key Events and Themes in Chapters 5-8
Summary of Chapters 5-8
Chapter 5 – Gatsby and Daisy Reunite
Nick arranges a meeting between Gatsby and Daisy at his house. Gatsby is extremely nervous but overjoyed when he finally sees Daisy again. They rekindle their feelings, and Gatsby takes her to his mansion to impress her with his wealth. Daisy is deeply moved, even crying over his expensive shirts, realizing what she could have had with him.
This chapter represents Gatsby’s dream coming true—at least for now.
Chapter 6 – Gatsby’s
Read MoreThe Great Gatsby: Story, Characters, and Jazz Age Background
The Great Gatsby: Plot Summary
Nick Carraway’s Arrival and First Encounters
Through the eyes of Nick Carraway, the narrator, we are introduced to his cousin, Daisy Buchanan, who is married to the aggressive and wealthy Tom Buchanan. Soon, the enigmatic Jay Gatsby appears as Nick’s mysterious neighbor. Gatsby lives in a huge mansion and hosts ultra-lavish parties attended by people who often don’t even know him. Gatsby spends much time in the evenings looking at a green light across the bay from his
Read MoreSymbols and Characters in The Great Gatsby
Symbols in The Great Gatsby
The Eyes of Dr. T.J. Eckleburg
The Eyes of Dr. T.J. Eckleburg are a pair of eyes with glasses painted on a billboard. The eyes represent God looking down and judging American society as a moral desert.
The Valley of Ashes
First introduced in Chapter 2, the Valley of Ashes between West Egg and New York is a long strip of land created by the dumping of industrial ashes. It represents the moral and social decline. The Valley of Ashes also symbolizes the plight of the poor, like
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