def question_eight(p1 = 0.0,
p2 = 0.0,
p3 = 0.0,
p4 = 0.0):
# ======= Reference =========
"""
# Result: State 1
a_11 = 0
a_12 = 0.5
a_13 = 0.5
a_14 = 1 / 3
# Result: State 2
a_21 = 1 / 3
a_22 = 0
a_23 = 0
a_24 = 1 / 3
# Result: State 3
a_31 = 1 / 3
a_32 = 0
a_33 = 0
a_34 = 1 / 3
# Result: State 4
a_41 = 1 / 3
a_42 = 0.5
a_43 = 0.5
a_44 = 0
"""
# ======= END Reference =========
# ======= Constants =========
p_values = [ p1, p2, p3, p4 ]
a_values = [ [0.0, 0.5, 0.5, 1.0 / 3.0],
[1.0 / 3.0, 0.0, 0.0, 1.0 / 3.0],
[1.0 / 3.0, 0.0, 0.0, 1.0 / 3.0],
[1.0 / 3.0, 0.5, 0.5, 0] ]
# ======= END Constants =========
return nth_period( p_values, a_values, 2 )[3]
def question_five(p1 = 0.0,
p2 = 0.0):
# ======= Reference =========
"""
# Result: State 1
a_11 = 2 / 3
a_12 = 1 / 2
# Result: State 2
a_21 = 1 / 3
a_22 = 1 / 2
"""
# ======= END Reference =========
# ======= Constants =========
p_values = [ p1, p2 ]
a_values = [ [ 2.0 / 3.0, 0.5 ],
[ 1.0 / 3.0, 0.5 ] ]
# ======= END Constants =========
return nth_period( p_values, a_values, 2 )[0]
