Question $2(30pt)$

Social experiment is conducted under the project of "Black Mirror". In this experimentation, modern

society, particularly with regard to the unanticipated consequences of new technologies are highlighted and

observed. At their last experiment, the volunteer is kept into a black museum and requested to find solutions

for complex cases. In the last case, data$-$set about the number of walking deads captured in the last four

months is shared and it is expected to make a forecast about upcoming months by using Moving Average

$(3$ months$).$ However, it is also known that for the same data$-$set, if anyone makes a forecast by using

Exponential Smoothing method $($with a value of $0,5$ for alpha constant$),$ forecasted values are always exactly

$25\%$ higher than the ones predicted by using MA $(3).$ Under these conditions, how do you comment on the

last $4$ months data$-$set? $($It is also known that expected number of captured walking dead is equal to $100$ in

the first month of this planning period$).$ Please explicitly show your calculations while solving the question.