= Solution
For independent charge arrivals described by a <Poisson distribution>, the one-sided <Shot noise> current <Power spectral density> is $S_I=2eI$. Treating the stated <bandwidth> as the <Effective noise bandwidth>,
$$
\boxed{i_{\rm rms}=\sqrt{2eI\Delta f}=\sqrt{2(1.6021766208\times10^{-19})(10^{-9})(10^5)}=5.66\times10^{-12}\,\mathrm A.}
$$
The expected rms noise is \b[$5.66\,\mathrm{pA}$], about $0.566\%$ of the mean current. This is the full <Shot noise> value with <Fano factor> one; correlations can suppress or enhance it. The elementary charge is from the external CODATA 2014 table.<CODATA recommended values of the fundamental physical constants 2014 by National Institute of Standards and Technology>[Elementary charge]{ref}
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