$**$Please show R code below thank you$**$

$1\mathrm{.}15(2$ point$)$ Let's work on getting conditional means now. What is the theoretical condi$-$

tional mean of $Y$ given $x?$

$1\mathrm{.}16(1$ point$)$ What is $E[Y|x=0]?$

$1\mathrm{.}17(1$ point$)$ Let's see how far is our sample from the theoretical sample. Given that we are

working with continuous random variables, it is unlikely that any of our observations has $x$ to

be exactly $0.$ But maybe we can include a bit of a range close to $0$ and see if we can plot that

distribution. To do that, first create a data frame data$2,$ which filters rows to have values of

$x$ between $-0\mathrm{.}25$ and $0\mathrm{.}25.$

$1\mathrm{.}18(1$ point$)$ Plot the histogram of $y$ for data$2$ to see if the values seem centered around

what we estimated in $1\mathrm{.}16.$

$1\mathrm{.}19(1$ point$)$ Estimate the average value of $y$ in data$2.$ How does this compare with

$0$