Consider X∼Bin(n,p)X\sim\text{Bin}(n,p)X∼Bin(n,p). Which of the following is \emph{incorrect}?
If npnpnp is an integer, then the mean and mode of this distribution coincide
If nnn is even and p=12p=\tfrac12p=21, then the median of this distribution is n/2n/2n/2
If P(X=k)=P(X=n−k)P(X=k)=P(X=n-k)P(X=k)=P(X=n−k) for every k∈{0,1,…,n}k\in\{0,1,\dots,n\}k∈{0,1,…,n}, then p=12p=\tfrac12p=21
If (n+1)p−1(n+1)p-1(n+1)p−1 is an integer, then this distribution is unimodal
