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$1$) ($1$ point) Use your knowledge of dice to generate a theoretical probability distribution of the possible sums obtained when rolling two dice. The first two rows have been completed for you.$\newline$Sum of dice $(\mathrm{X})$ \# of ways of obtaining sum Relative Frequency of $(\mathrm{X})=$$\newline$$\quad$$1$ way $(1+1) \quad 1 / 36$$\newline$$\quad$$2$ ways $(1+2,2+1) \quad 2 / 36$$\newline$$2$) ($1$ points) Use the theoretical data to calculate the mean, variance, and standard deviation of the theoretical probability distribution.$\newline$$3$) ($1$ point) Find the theoretical probability of rolling a sum less than $3$.$\newline$$4$) ($1$ point) Find the theoretical probability of rolling a sum between (and including) $4$ and $7$ .$\newline$$5$) ($1$ point) Visit the following website: http://www.dicesimulator.com/$\newline$and simulate $50$ rolls of two dice (or physically roll two dice $50$ times) and record your sums in the table below. You may also physically roll two dice $50$ times and record your sums.