GKI: 9-12-probabilistic methods

What is the conditional probability P(Y = y2 | X = x1)

• 2%

• 8%

• 20%

If X and Y are independent, are they also independent given any variables? I.e., if P(X|Y) = P(X), can we conclude that P(X|Y,Z) = P(X|Z)?

• yes

• no

If X and Y are independent, are they also independent given any variables? I.e., if P(X|Y) = P(X), can we conclude that P(X|Y,Z) = P(X|Z)?

• Yes

• No

Select the true statement

• D is a collider along the path A−D −E

• D is a collider along the path

  A−B −C −D −E

Select all correct statements:

• X is independent of Y

• X is independent of Y given E

• none of the options is correct

Select all correct statements:

• X is independent of Y

• X is independent of Y given E

• none of the options is correct

Select all correct statements:

• X is independent of Y

• X is independent of Y given E

• none of the options is correct

Select all correct statements:

• X is independent of Y

• X is independent of Y given E

• none of the options is correct

Select all correct statements:

• X is independent of Y

• X is independent of Y given E

• none of the options is correct

What is the one-step probability for $p_{0\ }=\ \left[1,0,0\right]^T$ ?

•  $p_{1\ }=\ \left[0.4,0.6,0\right]^T$  

•  $p_{1\ }=\ \left[0.4,0.4,0.2\right]^T$  

•  $p_{1\ }=\ \left[0,0.6,0.4\right]^T$  

•  $p_{1\ }=\ \left[0.6,0.2,0.2\right]^T$