Given 3 random variables
R: raining
T: Traffic
L: Late to school
a. Consider the relationship between R and T together marginal distribution and
conditional probability as following:
$R$
$P(R)$
$P(T|R)$
$+r$
0.1
$+r$
$+t$
0.8
$-r$
0.9
$+r$
$-t$
0.2
$-r$
$+t$
0.1
$-r$
$-t$
0.9
$T$
(5 pts) Compute the join distribution P(R, T)
b. Consider the relationship between R, T, L together marginal distribution and
conditional probability as following:
$R$
$P(R)$
$P(T|R)$
$P(L|T)$
$+r$
0.1
$+r$
$+t$
0.8
$+t$
$+l$
0.3
$+r$
$-t$
0.2
$+t$
$-l$
0.7
$-r$
0.9
$-r$
$+t$
0.1
$-t$
$+l$
0.1
$-r$
$-t$
0.9
$-t$
$-l$
0.9
$T$
$L$
(5 pts) Compute the join distribution P(R, T, L)
(5 pts) Compute the join distribution P(T, L)
(5 pts) Compute the marginal distribution P(L).