P(Y|X=x)&P_y(Y)

Discussion in 'CS1' started by ykai, Feb 27, 2023.

  1. ykai

    ykai Ton up Member

    Why is P(Y|X=x) equal to the marginal probability of Y without independent assumptions?
     
    ykai, Feb 27, 2023
    #1
  2. Andrea Goude

    Andrea Goude ActEd Tutor Staff Member

    is this from a section of the notes or a question in the notes?
     
    Andrea Goude, Feb 28, 2023
    #2
  3. ykai

    ykai Ton up Member

    This is CH03-Q4,it doesn't ask ,but I just wonder why is it?Is it a general case or special case? If it is general case,how could I prove it without independent assumption?
     
    Last edited: Feb 28, 2023
    ykai, Feb 28, 2023
    #3
  4. Andrea Goude

    Andrea Goude ActEd Tutor Staff Member

    Sorry still confused on the question, do you mean Ch04-Q4 conditional probabilities for M and N? they are independent so the conditional probability functions are equal to the marginals, see p14 of Ch04
     
    Andrea Goude, Feb 28, 2023
    #4
    ykai likes this.
  5. ykai

    ykai Ton up Member

    So equality is only true because of independence, right?
     
    ykai, Feb 28, 2023
    #5
  6. Andrea Goude

    Andrea Goude ActEd Tutor Staff Member

    Yes, correct
     
    Last edited: Feb 28, 2023
    Andrea Goude, Feb 28, 2023
    #6
    ykai likes this.

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