<Dd> f (k + 1) f (k) = (n − k) p (k + 1) (1 − p) (\ displaystyle (\ frac (f (k + 1)) (f (k))) = (\ frac ((n-k) p) ((k + 1) (1 - p)))). </Dd> <P> From this follows </P> <Dl> <Dd> k> (n + 1) p − 1 ⇒ f (k + 1) <f (k) k = (n + 1) p − 1 ⇒ f (k + 1) = f (k) k <(n + 1) p − 1 ⇒ f (k + 1)> f (k) (\ displaystyle (\ begin (aligned) k> (n + 1) p - 1 \ Rightarrow f (k + 1) <f (k) \ \ k = (n + 1) p - 1 \ Rightarrow f (k + 1) = f (k) \ \ k <(n + 1) p - 1 \ Rightarrow f (k + 1)> f (k) \ end (aligned))) </Dd> </Dl> <Dd> k> (n + 1) p − 1 ⇒ f (k + 1) <f (k) k = (n + 1) p − 1 ⇒ f (k + 1) = f (k) k <(n + 1) p − 1 ⇒ f (k + 1)> f (k) (\ displaystyle (\ begin (aligned) k> (n + 1) p - 1 \ Rightarrow f (k + 1) <f (k) \ \ k = (n + 1) p - 1 \ Rightarrow f (k + 1) = f (k) \ \ k <(n + 1) p - 1 \ Rightarrow f (k + 1)> f (k) \ end (aligned))) </Dd>

State the pmf and pdf of binomial distribution