lab2 EC

lab04/lab_2.py

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+'''
+Exercise 4.2
+@author isa3
+@version 28feb2020
+a.
+'''
+
+from probability import JointProbDist, enumerate_joint_ask
+
+# The Joint Probability Distribution Fig. 13.3 (from AIMA Python)
+P = JointProbDist(['Toothache', 'Cavity', 'Catch', 'Rain'])
+T, F = True, False
+P[T, T, T, T] = 0.054; P[T, T, F, T] = 0.006
+P[F, T, T, T] = 0.036; P[F, T, F, T] = 0.004
+P[T, F, T, T] = 0.008; P[T, F, F, T] = 0.032
+P[F, F, T, T] = 0.072; P[F, F, F, T] = 0.288
+P[T, T, T, F] = 0.054; P[T, T, F, F] = 0.006
+P[F, T, T, F] = 0.036; P[F, T, F, F] = 0.004
+P[T, F, T, F] = 0.008; P[T, F, F, F] = 0.032
+P[F, F, T, F] = 0.072; P[F, F, F, F] = 0.288
+
+
+'''
+i. My full joint probability distribution now contains 16 values.
+ii. The probabilities do sum up to 1.0; I acted as if P(Rain) was .5
+    and independent of the other variables, so I divided every 
+    original value in half. This resulted in the sum remaining equal
+    to 1 despite there being twice as many values.
+iii. I don't think you can use anything besides T or F values for
+    the random variables. The problem specified that the new random
+    variable Rain could only take on the values rain or not rain,
+    so it's either True that it's raining, or it's F, no in between.
+iv. Yes, the probabilities I chose indicated that the value of Rain
+    has a .5 chance of being True and a .5 chance of being False, 
+    regardless of what values are assigned to the original variables.
+'''
+
+''' 
+b.
+P(Toothache|Rain) = P(Tootache ^ Rain) / P(Rain)
+                  = (P[T, T, T, T] + P[T, F, T, T] + 
+                     P[T, T, F, T] + P[T, F, F, T]) /
+                    (P[T, T, T, T] + P[T, F, T, T] + 
+                     P[T, T, F, T] + P[T, F, F, T] +
+                     P[F, T, T, T] + P[F, F, T, T] + 
+                     P[F, T, F, T] + P[F, F, F, T])
+                  = (0.054 + 0.008 + 0.006 + 0.032) /
+                    (0.054 + 0.008 + 0.006 + 0.032 +
+                     0.036 + 0.072 + 0.004 + 0.288)
+                  = 0.1 / 0.5
+                  = 0.2
+
+'''
+PC = enumerate_joint_ask('Toothache', {'Rain': T}, P)
+print(PC.show_approx()) # result: False: 0.8, True: 0.2