Indicator variables Now we see how to compute it easily,by introducing some new random variables. Define Xi 0 if candidate i has been hired otherwise "Then X=∑1Xi. Recall the linearity of expectation: E[∑1X]=∑1E[X] ·We thus have E[X]=∑1E[x]. 6Indicator variables ◼ Now we see how to compute it easily, by introducing some new random variables. ◼ Define 𝑋𝑖 = ቊ 1 if candidate 𝑖 has been hired 0 otherwise . ◼ Then 𝑋 = σ𝑖=1 𝑛 𝑋𝑖 . ◼ Recall the linearity of expectation: 𝐄 σ𝑖=1 𝑛 𝑋𝑖 = σ𝑖=1 𝑛 𝐄 𝑋𝑖 ◼ We thus have 𝐄 𝑋 = σ𝑖=1 𝑛 𝐄 𝑋𝑖 . 6