Plotting Custom PDF in R
问题 Given: Consider the density function $\phi$ defined on $\mathbb{R}$ for $a\in \mathbb{R}$ and $b \in \mathbb{R}_+^\star$ such that $\forall x \in \mathbb{R}$ , $$ \phi(x; a,b) = \frac{1}{\sqrt{2\pi b^2}}e^{-\frac{1}{2}\left(\frac{x-a}{b}\right)^2}. $$ Consider now the so-called Bart Simpson probability density function $f$ given by \begin{eqnarray} \label{eq:bart:1d:1} f(x) = \frac{1}{2}\phi(x; 0,1) + \frac{1}{10}\sum_{j=0}^4{\phi(x; (j/2)-1, 1/10)}. \end{eqnarray} Questions: Plot the pdf $f$