Considerthe mode m ofthe binomial $($n$,$p$)$ distribution. Use the formula m $=$ int $($np$+$ p$)$ to show the following:$$a$)$ If np happens to be an integer, then m $=$ np$.$ b$)$ If np is not an integer, then the most likely number of successes m is one of the$$two integers to either side of np$.$c$)$ Show by examples that m is not necessarily the closest integer to np$.$ Neither is m always the integer above np$,$ nor the integer below it$.$