[Tex/LaTex] Customized enumerate items

Question

I want to write following on my latex. Please help me.

\documentclass[12pt,oneside,a4paper]{report}
\pagestyle{plain}
\usepackage{enumerate}
\usepackage{amsmath}
\usepackage{graphicx}
\usepackage{setspace}
\usepackage{bm}
\usepackage{mathdesign}
\usepackage{amsthm}
\usepackage{amssymb}
\usepackage{glossaries}
\usepackage{enumitem}
\makeglossaries
\newtheorem{theorem}{Theorem}[section]
\newtheorem{corollary}{Corollary}[section]
\newtheorem{lemma}{Lemma}[section]
\newtheorem{defn}{Definition}[section]
\newtheorem{remk}{Remark}[section]
\newtheorem{assump}{Assumptions}[section]
\numberwithin{equation}{section}
\setlength{\topmargin}{-.7in}
\setlength{\textheight}{9.5in}
\setlength{\oddsidemargin}{-.3in}
\setlength{\textwidth}{7in}
\renewcommand{\qedsymbol}{$\blacksquare$}
\begin{document}\begin{theorem}
If the $(k\times 1)$ vector $\bm{x}$ is distributed normally with mean vector $\bm{\mu}$ and variance-covariance matrix $\bm{I}_k$, then
\begin{enumerate}[(i).]
\item $\mathbb{E}[\phi(\bm{x}'\bm{x})\bm{x}]=\bm{\mu}\mathbb{E}[\phi(\chi^{2}_{(k+2,\Delta)})]$,
\item $\mathbb{E}[\phi(\bm{x}'\bm{x})\bm{x}\bm{x}']=\bm{I}_{k}\mathbb{E}[\phi(\chi^{2}_{(k+2,\Delta)})]+\bm{\mu}\bm{\mu}'\mathbb{E}[\phi(\chi^{2}_{(k+4,\Delta)})]$
\end{enumerate}
where $\Delta=\frac{1}{2}\bm{\mu}'\bm{\mu}$ is the noncentrality parameter.
\end{theorem}
 \begin{assump}[Regularity Conditions]
\begin{enumerate}[start=0,label={(\bfseries R\arabic*):}]
\begin{enumerate}
\item The pdfs are distinct.
\item The pdfs have common support for all $\theta$.
\end{enumerate}
\end{assump}
\end{document}

Answer 1

Without further information this is a starter...(I've not done the theorem environment around the enumeration)

The enumitem package is the key for easy customization of itemize/enumerate lists. It provides the means for use a starter value (start=0) and the label=.... option.

enumitem can be used together or as enumerate using the shortlabels option.

\documentclass{article}
\usepackage{enumerate}
\usepackage[shortlabels]{enumitem}

\begin{document}

% Traditional style
\begin{enumerate}[a)] 
\item This is
\item an easy
\item customization of standard enumerate
\end{enumerate}


\begin{enumerate}[start=0,label={(\bfseries R\arabic*):}]
\item This is
\item an easy
\item customization of enumerate
\end{enumerate}
\end{document}