If I know P(x) and P(y|x), how can I know P(y)?If I need to compute P(y) and I only know P(y|x) and P(x).I know that:P(y|x)=P(y,x)P(x)This is the contingency table for P(y|x): P(y|x) | +x | ⌝x |------------------------- +y | 0.91 | 0.03 |------------------------- ⌝y | 0.09 | 0.97 |-------------------------And the probability of x: | +x | ⌝x |------------------------- P(x) | 0.05 | 0.95 |-------------------------How can I compute P(y)?

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If I know P(x) and P(y|x), how can I know P(y)?If I need to compute P(y) and I only know P(y|x) and P(x).I know that:P(y|x)=P(y,x)P(x)This is the contingency table for P(y|x): P(y|x) |   +x   |    ⌝x  |-------------------------   +y   |  0.91  | 0.03 |-------------------------     ⌝y   |  0.09  | 0.97 |-------------------------And the probability of x:        |   +x   |    ⌝x  |-------------------------  P(x)  |  0.05  | 0.95 |-------------------------How can I compute P(y)?

Chaya Proctor · Accepted Answer

P  (  y  ,  x  )  =  P  (  y      |    x  )  P  (  x  )  P  (  y  )  =      ∑    x    P  (  y  ,  x  )  =      ∑    x    P  (  y      |    x  )  P  (  x  )

If I know P(x) and P(y|x), how can I know P(y)? If I need to compute P(y) and I only know P(y|x) and P(x). I know that: P(y|x)=P(y,x)P(x) How can I compute P(y)?

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