Question

Let 𝑌 ∼ 𝑁𝑜𝑟𝑚𝑎𝑙(3, 1), 𝑊 ∼ 𝑁𝑜𝑟𝑚𝑎𝑙(1, 2) and 𝑋 ∼ 𝐵𝑒𝑟𝑛𝑜𝑢𝑙𝑙𝑖 (𝑝 = 0.9) where 𝑋 = 1 is success and 𝑋 = 0 is failure. Let 𝑆 = 𝑋𝑌 + (1 − 𝑋)𝑊. Then 𝐸(𝑆) = _________ (round off to 1 decimal place)

Answer 1

The correct answer is: 2.7 or 2.9 (approx.)