 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2016/discrete-mathematics-continuous-mathematics-and-probability/7/a/i/solution

The

X_{i}

p

. Their sum has the binomial distribution $S_{n} \sim Bin (n, p)$ , whose probability mass function is

P (S_{n} = k) = (k n) p^{k} (1 - p)^{n - k}, k = 0, \dots, n .

Choose the

k

successful events in

(k n)

ways; independence gives the same product probability for each choice. At

p = 0

p = 1

, interpret the formula by its degenerate distribution or by continuity.

 New to topics? Read the docs here!