Multiplying random variables

Foundations of Probability in R

David Robinson

Chief Data Scientist, DataCamp

Multiplying a random variable

$$X \sim \text{Binomial}(10, .5)$$

$$Y \sim 3 \cdot X$$

$$X \sim \text{Binom}(10, .5)$$

$$Y=3\cdot X$$

X <- rbinom(100000, 10, .5)

mean(X)
# [1] 5.006753

Y <- 3 * X

mean(Y)
# [1] 15.02026

$$E[k \cdot X]=k \cdot E[X]$$

$$X \sim \text{Binom}(10, .5)$$

$$Y=3\cdot X$$

X <- rbinom(100000, 10, .5)

var(X)
# [1] 2.500388

Y <- 3 * X

var(Y)
# [1] 22.50349

$$\text{Var}[k \cdot X]=k^2 \cdot \text{Var}[X]$$

$$E[k\cdot X] = k \cdot E[X]$$

$$\text{Var}(k \cdot Y) = k^2 \cdot \text{Var}(X)$$

Foundations of Probability in R