Question: A loaded coin has a 75% chance of coming up heads. Let X be the number of heads in 8 indepen­dent flips of this coin.

(a) Compute \(\Pr \left( X=5 \right)\), \(\Pr \left( X\le 5 \right)\) and \(\Pr \left( 3\le X\le 6 \right)\)

(b) Build pmf(X) and cdf(X) (note that this does not ask for the empirical CDF but for the true CDF)