R 的機率基礎
David Robinson
Chief Data Scientist, DataCamp
$$X \sim \text{Binom}(10, .5)$$
$$Y \sim \text{Binom}(100, .2)$$
$$Z \sim X + Y$$
X <- rbinom(100000, 10, .5) mean(X) # [1] 5.00938
Y <- rbinom(100000, 100, .2) mean(Y) # [1] 19.99422
Z <- X + Y mean(Z) # [1] 25.0036
$$E[X+Y]=E[X]+E[Y]$$
X <- rbinom(100000, 10, .5) var(X) # [1] 2.500895
Y <- rbinom(100000, 100, .2) var(Y) # [1] 16.06289
Z <- X + Y var(Z) # [1] 18.58055
$$\text{Var}[X+Y]=\text{Var}[X]+\text{Var}[Y]$$
$$\text{（即使 X 與 Y 不獨立也成立）}$$
$$\text{（僅在 X 與 Y 獨立時成立）}$$
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