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Here is my problem statement:

Let $X=(X_1,X_2)∈[0,1]×[0,1]$ and $Y∼Bernoulli(p=X_1⋅X_2)$. Plot the Bayes decision boundary ${(x1_,x_2):P(Y=1|X=(x_1,x_2))=0.5}$ and indicate the regions in $[0,1]×[0,1]$ whose points would be classified as 0 and 1.

Do we need to write a discriminant function to plot the decision boundary? I am kinda confused. I appreciate your time. Thanks!

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  • $\begingroup$ Yeah, solve for $p(y=0|x)=p(y=1|x)$ $\endgroup$
    – gunes
    Commented Sep 14, 2020 at 15:08
  • $\begingroup$ @gunes Would you please elaborate on it a littel bit more. $\endgroup$
    – ADAM
    Commented Sep 24, 2020 at 14:21
  • $\begingroup$ @ADAM What I did, I generated X1 and X2 and compute p=X1.X2. Then Plot them and see the separation based on the probability threshold. Like Class 1 if p>0.5 else class 0. $\endgroup$ Commented Sep 24, 2020 at 22:50
  • $\begingroup$ I am curious to see it mathematically like the LDA discriminant function. $\endgroup$ Commented Sep 24, 2020 at 22:51
  • $\begingroup$ Would you show me how did you produce the graph either in R or Python $\endgroup$
    – ADAM
    Commented Sep 25, 2020 at 0:16

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