$4.$ Suppose we generate letters with the following probability distribution. We then encode our string of letters into a file by replacing each letter with its codeword bitstring, which are concatenated together into the resulting binary message.

$1.$ Decode the bitstring $"\backslash (01010011011010001"\backslash )$ into a string of letters.

$2.$ Encode the string BEADED into a bitstring

$3.$ Use this probability distribution to compute the

entropy $\backslash ($ H$($L$)\backslash )$ of a single letter.

$4.$ Compute the expected length of a random letter's codeword.

$5.(560)$ Randomly generate $100$ symbols, independently, with this distribution $($it helps to use a computer for this, but you do you.$)$ Encode your $100-$symbol string as a bitstring using this table, and determine the length in bits of that bitstring. How does this compare to your answers from $(3)$ and $(4)?$