📗 -> 11/26/24: Name


[Lecture Slide Link]

🎤 Vocab

❗ Unit and Larger Context

Covering:

  • Two tail hypothesis
  • Markov Chain

✒️ -> Scratch Notes

DIVC

7820
71015
271
3201

  1. read data
  2. naming columns
  3. cleaning
  4. 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 area.

  • 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 (RV value at time ) is called state
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
  • 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.
Link to original

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:

Resources

  • Put useful links here

Connections

  • Link all related words