MathProbabilityDiscrete random variables

Expected value of discrete random variable

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\mathbb{E}a \leq \mathbb{E}b \Rightarrow \forall c (\text{random variable}) \; \mathbb{E}(a + c) \leq \mathbb{E}(b + c)

\mathbb{E}a \leq \mathbb{E}C \Rightarrow \forall x \; a(x) \leq C, \text{where } C - Const

\mathbb{E}a \leq \mathbb{E}b \Rightarrow \mathbb{E}(5 \cdot a) \leq \mathbb{E} (5 \cdot b)

\mathbb{E}a \leq \mathbb{E}(a + b) \Rightarrow \mathbb{E}b \geq 0

\mathbb{E}a \leq \mathbb{E}b \cdot \mathbb{E}c \Rightarrow \mathbb{E}a \leq \mathbb{E}b + \mathbb{E}c

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