Exercise $2$

In the next exercise, you will implement the function to compute $($word$$spam$)$ and $($word$$ham$).$ Since the computations are the same for both types of emails, you will create a function to compute $($word$$class$)$ where class can be either spam $(1)$ or $($ham$)0.$

Expected Output $($the results may vary in the last decimal places$)$

P$($lottery $|$ spam$)=0\mathrm{.}00807899461400359$

P$($lottery $|$ ham$)=0\mathrm{.}0002883506343713956$

P$($schedule $|$ spam$)=0\mathrm{.}008976660682226212$

P$($schedule $|$ ham$)=0\mathrm{.}10294117647058823$In $[]$: def prob$\_$word$\_$given$\_$class$($word$,$ cls$,$ word$\_$frequency, class$\_$frequency$)$:

Calculate the conditional probability of a given word occurring in a specific class.

Parameters:

word $($str$)$: The target word for which the probability is calculated.

cls $($str$)$: The class for which the probability is calculated, it may be 'spam' or 'ham'

word$\_$frequency $($dict$)$: The dictionary containing the words frequency.

class$\_$frequency $($dict$)$: The dictionary containing the class frequency.

Returns:

float: The conditional probability of the given word occurring in the specified class.

$"\text{'}"!$

### START CODE HERE ###

# Get the amount of times the word appears with the given class $($class is stores in spam variable$)$

amount$\_$word$\_$and$\_$class $=$ word$\_$frequency $[$None$][$None$]$

p$\_$word$\_$given$\_$class $=$ None$/$cl$$ss$\_$frequency $[$None$]$

### END CODE HERE ###

return p$\_$word$\_$given$\_$class

In $[]$:

print$($f$"$P$($lottery $|$ spam$)=\{$prob$\_$word$\_$given$\_$class$(\text{'}$lottery$\text{'},$ cls $=$ 'spam', word$\_$frequency $=$ word$\_$frequency, class$\_$f

print$($f$"$P$($lottery $|$ ham$)=\{$prob$\_$word$\_$given$\_$class$(\text{'}$lottery$\text{'},$ cls $=$ 'ham', word$\_$frequency $=$ word$\_$frequency, class$\_$fre

print$($f$"$P$($schedule $|$ spam$)=\{$prob$\_$word$\_$given$\_$class$(\text{'}$schedule$\text{'},$ cls $=$ 'spam', word$\_$frequency $=$ word$\_$frequency, class

print$($f$"$P$($schedule $|$ ham$)=\{$prob$\_$word$\_$given$\_$class$(\text{'}$schedule$\text{'},$ cls $=$ 'ham', word$\_$frequency $=$ word$\_$frequency, class$\_$f

Expected Output $($the results may vary in the last decimal places$)$