C2 - linearity of expectation

linearity of expectation

E [X + Y] = E [X] + E [Y]

E [f (X) + g (Y)] = E [f (X)] + E [g (Y)]

E [X] = E [X_{1}] + E [X_{2}] + \dots + E [X_{n}] = n E [X_{i}] = n p

here, $X_{i}$ 's are called the indicator random variables as they take on the values $0$ or $1$