Exercise $5.$ Consider the following Hidden Markov Model $($HMM$)$

In your answers below, describe how you would design an auto$-$corrector for keyboard input using this model. For simplicity, assume the lengths of the intended and typed character sequences are the same.

a$.$ What do the evidence variables $\backslash ($ E$\_\{$t$\}\backslash )$ represent in this application?

b$.$ What do the hidden variables $\backslash ($ X$\_\{$t$\}\backslash )?$ represent? What are the range of possible values?

c$.$ Describe the meaning of $\backslash ($ P$\backslash$left$($E$\_\{$t$\}\backslash$mid X$\_\{$t$\}\backslash$right$)\backslash ).$ Describe how would you specify it$,$ i$.$e$.$ go about determining or

defining the values. Note this is not how you would infer $\backslash ($ E$\_\{$t$\}\backslash ),$ but rather how you would specifiy the values that define the probabilty function for $\backslash ($ P$\backslash$left$($E$\_\{$t$\}\backslash$mid X$\_\{$t$\}\backslash$right$)\backslash ).$