Show all your work. Just giving an answer without an explanation will not be accepted as a solution. You mus provide necessary explanations and solve the questions by using the techniques$/$methods$/$results covered in cla During the exam, using communication devices is strictly forbidden. For each question, you need to compute final numerical value. Students can use one page cheat sheet $($A$4-$size, two$-$sided$).$ The cheat sheet must be handwritten by the student. Photocopy, print$-$out, etc. will not be accepted. The cheat sheets will be collected end of the exam. Exam duration: $65$ minutes.

Let the joint probability density function of the continuous random variables $x_1$ and $x_2$ be

$x_{1}P\{x_1>1\}P\{x_2>1|x_1=1\mathrm{.}5\}E[x_1]Cov(x_1,x_1)E[x_2]E[x_1{x}_2]Cov(x_1,x_2)$