📗 -> 11/26/24: Name
[Lecture Slide Link]
🎤 Vocab
❗ Unit and Larger Context
Covering:
- Two tail hypothesis
- Markov Chain
✒️ -> Scratch Notes
DIVC
| 7 | 8 | 20 |
|---|---|---|
| 7 | 10 | 15 |
| 2 | 7 | 1 |
| 3 | 20 | 1 |
- read data
- naming columns
- cleaning
- add # of times a message. i_mit-dat
Hypothesis Testing
Berk:
Davis:
Believe the two means are equal
But Sample:
Two Tail Test Ha:
In the Z-world, alpha of .05 gives:
Fail to reject null for laternative, w/ alpha=.05. 10 > -39 AND p-value of
p-value 2(
Areas of Rejection: If the z score is more surprising than our
- For
and two-tailed, it needs to cover 0.025 area on both side, and z score more surprising than
Markov Chains
Random Variables through time
, state of RV at time
outcome at
Sample Space: set of states the variable can take on.
- In this context, its the State Space
Markov Chain / Markov Process
- The Markov Process property states that the probability of transitioning from one state to another is the same regardless of the states that preceded it.
Quick Refresher
Matrix Demonstration
Intuition
: The element in the i-th row and j-th column of the result matrix C. : The element in the i-th row and k-th column of A. : The element in the k-th row and j-th column of B. Widths and Heights
Link to original
- i: Corresponds to the height of A (its rows) and is used to determine the rows of C.
- j: Corresponds to the width of B (its columns) and is used to determine the columns of C.
- k: Corresponds to the width of A (or the height of B), which must be the same for multiplication to be defined.
2 state Markov Chain Formula:
- Start with probability of states x and y
- Multiply by transition probability matrix
- End with probabilities of states x and y
- Solve system of equations if needed
- Helped by the fact that the state probabilities must sum to 1
Protein Example
Given X_0=gene, what is P(X_2=gene)?
Finding Steady State:
🔗 -> Links
Resources
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Connections
- Link all related words