Consider the sequence of distribution functions \(\left\{F_{n}ight\}_{n=1}^{\infty}\) where

\[F_{n}(x)= \begin{cases}0 & x<0 \\ \frac{1}{2}+(n+2)^{-1} & 0 \leq x<1 \\ 1-(n+2)^{-1} & x \geq 1\end{cases}\]

a. Specify a function \(G\) such that \(F_{n} \leadsto G\) as \(n ightarrow \infty\) and \(G\) is a right continuous function.

b. Specify a function \(G\) such that \(F_{n} \leadsto G\) as \(n ightarrow \infty\) and \(G\) is a left continuous function.

c. Specify a function \(G\) such that \(F_{n} \leadsto G\) as \(n ightarrow \infty\) and \(G\) is neither right continuous nor left continuous.