As a financial analyst, you evaluate financial data and extract relevant information to make investment recommendations. This time, you are tasked with analyzing NVIDIA based on its historical prices. $(15$ points$)$

$\backslash$table$[[$Year$,$Price,Dividend$],[2000,0\mathrm{.}77,0],[2001,2\mathrm{.}15,0],[2002,5\mathrm{.}48,0],[2003,0\mathrm{.}86,0],[2004,1\mathrm{.}85,0],[2005,1\mathrm{.}91,0],[2006,3\mathrm{.}75,0],[2007,5\mathrm{.}11,0],[2008,6\mathrm{.}15,0],[2009,1\mathrm{.}99,0],[2010,3\mathrm{.}85,0],[2011,5\mathrm{.}98,0],[2012,3\mathrm{.}69,0\mathrm{.}12],[2013,3\mathrm{.}07,0\mathrm{.}12],[2014,3\mathrm{.}93,0\mathrm{.}12],[2015,4\mathrm{.}80,0\mathrm{.}12],[2016,7\mathrm{.}32,0\mathrm{.}12],[2017,27\mathrm{.}30,0\mathrm{.}16],[2018,61\mathrm{.}45,0\mathrm{.}16],[2019,35\mathrm{.}94,0\mathrm{.}16],[2020,59\mathrm{.}11,0\mathrm{.}16],[2021,129\mathrm{.}90,0\mathrm{.}16],[2022,244\mathrm{.}86,0\mathrm{.}16],[2023,195\mathrm{.}37,0\mathrm{.}16],[2024615\mathrm{.}27,0\mathrm{.}16,]]$

a$)$ If a client invested $$10,000$ at the beginning of $2000,$ what is the total dollar return for that client, measured at the beginning of $2024?$

b$)$ What is the typical $($average$)$ return over the $24-$year period?

c$)$ What is the average compound return per year over the $24-$year period?

d$)$ Obtain the variance and standard deviation of returns.

e$)$ If the average risk$-$free rate during this period was $4\mathrm{.}5\%,$ what is Nvidia's risk premium? How can we interpret this number?