Written Wоrk Scаnning Instructiоns:Scаn eаch sheet оf your written work. You may use a scanner or your phone/tablet camera to scan your work. NOTE: problems with only a correct answer and none of the correct work receive a maximum of 1 point out of 10, so be sure you include any necessary supporting work!If using a phone, tablet, or document scanner for scanning, transfer your file(s) onto your computer with Honorlock running. You can use the UND email or OneDrive tab that you opened in Step 1 or a desktop app such as ICloud or Dropbox or Google Drive. Note: Honorlock will not allow you to access other cloud drives through a browser. Create a PDF file of your written work - combine images into a single PDF file. You can do so by using your scanner's installed software, directly on your phone using a scanning app, or using a desktop application such as MS Word or Pages. Note: Honorlock will block access third party websites (such as combinePDF.com) to combine and create a single PDF.Once you have the PDF file on your computer's local drive, open it and scroll through each page slowly to record an image of your work on the Honorlock sccreen recording. Make sure to complete this step carefully since this may be used a backup in case of file corruption/Blackboard issues.Answer the Yes/No question below and proceed to the next question. DO NOT SUBMIT OR CLOSE THIS BLACKBOARD EXAM before answering all the questions.Confirm this question below: I have created a single PDF of my written work and scrolled through it on my computer to record images of it on my Honorlock recording.
Prоblem 1: Cоmputing а PDF frоm а CDF (25 points) Find the PDF of the following CDF, where (phi(x)) is the CDF of а standard Gaussian. begin{align} F_X(x) = begin{cases} 0 & x < 0 \ phi(x) & x geq 0 end{cases} end{align} Write out the definition of a median, and find the median of the random variable X. Problem 2: The Sum of Two Independent Random Variables (25 points) Let (X sim text{Uniform}(-1,1)) and (Y) have the PDF (f_Y(y) = e^y) for (y < 0). Let (Z = X + Y). Find the PDF Z. Problem 3: Conditional Expectation (25 points) Let (X sim text{Exponential}(lambda)) and (Y | X=x sim text{Exponential}(frac{1}{x})). Find (mathbb{E}left[YX e^{-Y/X}right]). Problem 4: The Transformation of Two Random Variables (25 points) Say (X) has the PDF (f_X(x) = -xe^x) for (x < 0), and let (Y sim text{Uniform}(0,1)). Set (Z = XY) and find the PDF of (Z). Congratulations, you are almost done with Midterm 2. DO NOT end the Honorlock session until you have submitted your work to Gradescope. When you have answered all questions: Use your smartphone to scan your answer sheet and save the scan as a PDF. Make sure your scan is clear and legible. Submit your PDF to Gradescope as follows: Email your PDF to yourself or save it to the cloud (Google Drive, etc.). Click this link to go to Gradescope to submit your work: Midterm 2 - OUS Students Return to this window and click the button below to agree to the honor statement. Click Submit Quiz to end the exam. End the Honorlock session.