You are given the prior distribution P(X), and two conditional distributions P (Y |X) and P (Z|Y) as below (you are also given the fact that Z is independent from X given Y). All variables are binary variables. Compute the table of their joint distribution based on the chain rule. Your might round your answers to 4 decimal places. (4 Points) X P(X)
0 0.1
1 0.9
Y X P(Y|X)
0 0 0.600
1 0 0.400
0 1 0.500
1 1 0.500
Z Y P(Z|Y)
0 0 0.400
1 0 0.600
0 1 0.800
1 1 0.200
X Y P(X, Y)
0 0
1 0
0 1
1 1
X Y Z P(X, Y,Z)
0 0 0
1 0 0 0.18
0 1 0 0.032
1 1 0
0 0 1 0.036
1 0 1
0 1 1 0.008
1 1 1

step-by-step explanation:

given that ab is divided into equal parts as

ac, cd, de, ef, fg, gh, hi, ib.

from this we find that f is the midpoint of ab.

so using mid point formula we find

f = (3,7)

similarly considering fb, we get

h = mid point of fb = ((6,6) and g, mid point of fh is

g = (9/2, 13/2)

i is mid point of hb

so i =(15/2,11/2)

shell's the art director at her local community center. she paid $10 and for each child that attends she earns $4.

for each child she ears $4 that is the slope m = 4

she paid $10, that is the initial amount paid. so 10 is the y intercept b

m =4   and b = 10

y intercept is 10 so the point is (0,10)

we start graph from y intercept (0,10)

slope = 4 . we know slope = rise / run

slope = 4   or 4/1   are same

rise = 4   and run = 1

for rise we move 4 units up and for run we move 1 unit to the right

the graph is attached below

x axis is the number of child she attends

y axis is the amount   she earns