A discrete memoryless information source has the alphabet $\{$a$1,$ a$2,$ a$3,$ a$4,$ as$\}$ with the corresponding probabilities $\{0\mathrm{.}1,0\mathrm{.}2,0\mathrm{.}05,0\mathrm{.}3,0\mathrm{.}35\}.1.$ Can this source be compressed at a rate of $2$ bits per source symbol such that lossless reconstruction of it is possible? $2.$ Now consider all sequences of length $1000$ that this source can generate. How many of these sequences are possible? Write your answer in exponential form. $3.$ Approximately how many of the sequences in Part $2$ are typical sequences? Write your answer in exponential form. $4.$ Now assume that you want to merge two letters of the source into one new letter b$,$ say, b $=\{$a;$,$ aj$\},$ such that the resulting source $($which now has four outputs instead of five$)$ can be compressed at a rate of $1\mathrm{.}5$ bits per symbol and can be recovered with no loss. Which two letters would you merge into the new letter b$?$