prob_of_sign = .25
weight_probs = {  # this is the solution they prefer
    '3': prob_of_sign,
    '3': prob_of_sign,
    '2': prob_of_sign,
    '5': prob_of_sign
}
expectation = sum(
    [int(x_i)*weight_probs[x_i] for x_i in weight_probs]
)
expectation_of_squares = sum(
    [int(x_i)*int(x_i)*weight_probs[x_i] for x_i in weight_probs]
)
square_of_expectation = expectation**2
variance = expectation_of_squares - square_of_expectation
print('Expected value:', expectation)
print('Variance:', variance)