Need to use google co$-$lab for this question, and use the R compiler, not Python. Given data: horse$\_$data$=$c$(0,2,2,1,0,0,1,1,0,3,0,2,1,0,0,1,0,1,0,1,$

$0,0,0,2,0,3,0,2,0,0,0,1,1,1,0,2,0,3,1,0,0,$

$0,0,2,0,2,0,0,1,1,0,0,2,1,1,0,0,2,0,0,0,0,$

$0,1,1,1,2,0,2,0,0,0,1,0,1,2,1,0,0,0,0,1,0,$

$1,1,1,1,0,0,0,0,1,0,0,0,0,1,1,0,0,0,0,0,0,$

$2,1,0,0,1,0,0,1,0,1,1,1,1,1,1,0,0,0,1,0,2,$

$0,0,1,2,0,1,1,3,1,1,1,0,3,0,0,1,0,1,0,0,0,$

$1,0,1,1,0,0,2,0,0,2,1,0,2,0,1,0,0,0,1,0,0,$

$1,0,0,0,0,1,0,0,0,1,1,0,1,0,0,0,0,0,2,1,1,$

$1,0,2,1,1,0,1,2,0,1,0,0,0,0,1,1,0,1,0,2,0,$

$2,0,0,0,0,2,1,3,0,1,1,0,0,0,0,2,4,0,1,3,0,$

$1,1,1,1,2,1,3,1,3,1,1,1,2,1,1,3,0,4,0,1,0,$

$3,2,1,0,2,1,1,0,0,0,1,0,0,0,0,0,1,0,1,1,0,$

$0,0,2,2,0,0,0,0)$ a$)$ Plot the frequencies of the counts present in the data.

b$)$ Calculate $\backslash$lambda $1$ and $\backslash$lambda $2($from problem $2,$ given in imagehat$({)}_1=\frac{1}{n}{\displaystyle \underset{i=1}{\overset{n}{}}}{x}_i,$hat$({)}_2=\frac{1}{n}{\displaystyle \underset{i=1}{\overset{n}{}}}(x_i-(\stackrel{}{x}){)}^2)$ for the data.

c$)$ Plot the p$.$m$.$f$.$ of the Poisson distribution with respect to $\backslash$lambda $1$ and $\backslash$lambda $2$ on top of the frequency plot $($give the two p$.$m$.$f$.$s different colors in order to tell which one is which$)$ Which estimate fits the data better?