import numpy as np

x = np.array([-1, 3, 7, 10, 12, 27.]) # values in sample space
fx = np.array([2, 1, 1, 2, 3, 1]) / 10 # density at those values

Calculate

\[\mathbb{E}[X] = \sum_{x \in S} x f(x)\]

m = np.sum(x * fx)
m

9.1

Calculate

\[\mathbb{V}[X] = \mathbb{E}[(X - \mathbb{E}[X])^2] = \sum_{x \in S} (x - m)^2 f(x)\]

np.sum((x - m) ** 2 * fx)

59.28999999999999

Calculate

\[\mathbb{P}[X > m] = \sum_{x \in S} 1_{\{10, 12, 27\}}(x) f(x)\]

ind = x > m
np.sum(fx[ind])

0.6