The sequence (left{frac{1}{n} ight}_{n=1}^{infty}) converges to 0 . If we treat each constant, (frac{1}{n}), as a constant

The sequence \(\left\{\frac{1}{n}\right\}_{n=1}^{\infty}\) converges to 0 . If we treat each constant, \(\frac{1}{n}\), as a constant random variable, then the corresponding \(\mathrm{CDF}\) is

\[F_{n}(x)=\left\{\begin{array}{l}0 \text { if } x<\frac{1}{n} \\1 \text { if } x \geq \frac{1}{n}\end{array}\right.\]

Show that the sequence also converges to 0 in distribution and probability. Note, however, that \(F_{n}(0)=0\) for all \(n\), but \(F(0)=1\), where \(F\) is the CDF of constant 0 .