variance and E

hsy_rvalue = pd.Series([-7.40,
-6.20,
-5.00,
-3.80,
-2.60,
-1.40,
-0.20,
1.00,
2.20,
3.90,
])
hsy_prob = pd.Series([0.20,
0.00,
0.00,
0.40,
2.39,
13.72,
46.52,
30.42,
5.37,
0.99,
])

def expected_value(data_rvalue, data_prob):
    '''Данная функция находит математическое ожидание'''
    E = 0
    for x in range(len(data_rvalue)):
        E += data_rvalue[x] * data_prob[x]
    return E
expected_value(hsy_rvalue, hsy_prob)
# OUTPUT: 8.369000000000003

def variance(data_rvalue, data_prob):

    '''Данная функция находит дисперсию'''

    rvalue_probs = dict(zip(data_rvalue, data_prob))
    expectation = expected_value(data_rvalue, data_prob) # E(X)
    square_of_expectation = expectation ** 2 # (E(X))^2
    expectation_of_squares = expected_value(data_rvalue**2, data_prob) # E(X^2)
    variance = expectation_of_squares - square_of_expectation # E(X^2) - (E(X))^2

    return variance

variance(hsy_rvalue, hsy_prob)
# OUTPUT: 63.06493899999994

def standard_dev(data_rvalue, data_prob):
    v = variance(data_rvalue, data_prob)
    standard_dev = math.sqrt(v)
    return standard_dev
standard_dev(hsy_rvalue, hsy_prob)
# OUTPUT: 7.94134365205284

lisn_rvalue = [-3.53,
-2.59,
-1.66,
-0.72,
0.22,
1.16,
2.10,
3.04,
3.97,
5.22
]
lisn_prob = [1.19,
3.75,
10.87,
23.12,
32.61,
18.58,
6.92,
1.98,
0.59,
0.40
]

expected_value(lisn_rvalue, lisn_prob)
# OUTPUT: 5.104700000000004

variance(lisn_rvalue, lisn_prob)

# ---------------------------------------------------------------------------
# TypeError                                 Traceback (most recent call last)
# /tmp/ipykernel_27/1282851349.py in <module>
# ----> 1 variance(lisn_rvalue, lisn_prob)

# /tmp/ipykernel_27/325116310.py in variance(data_rvalue, data_prob)
#       6     expectation = expected_value(data_rvalue, data_prob) # E(X)
#       7     square_of_expectation = expectation ** 2 # (E(X))^2
# ----> 8     expectation_of_squares = expected_value(data_rvalue**2, data_prob) # E(X^2)
#       9     variance = expectation_of_squares - square_of_expectation # E(X^2) - (E(X))^2
#      10
#
# TypeError: unsupported operand type(s) for ** or pow(): 'list' and 'int'