STAT 3360-HOMEWORK 4-THE NUMBER (X) OF CARS SOLD BY A RANDOMLY

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STAT 3360-HOMEWORK 4-THE NUMBER (X) OF CARS SOLD BY A RANDOMLY

HOMEWORK 4 – STAT 3360 – FALL 2016DUE BY SEPTEMBER 29PLEASE, SUBMIT THIS DOCUMENT AND SHOW YOUR FIRST AND LAST NAME BELOW!STAPLE OR PAPERCLIP YOUR WORK, PLEASE!PLEASE, READ GK SECTIONS 7.1 – 7.3 BEFORE SOLVING THESE EXERCISES.SECTION002FIRST NAMELAST NAMEPROBLEM 1 [30 POINTS = 5 + 10 + 15]THE NUMBER (X) OF CARS SOLD BY A RANDOMLY SELECTED DEALERSHIP IN THEMETROPLEX AREA DURING ONE DAY HAS A DISTRIBUTION SHOWN BELOW.X = NUMBER OF CARS SOLD PROBABILITY20.1530.3040.2550.2060.101.DETERMINE THE EXPECTED VALUE OF X.E [X] =2.WHAT IS THE VARIANCE OF X?VAR [X] =3.THE COMMISSION IS DEFINED (IN $1,000) AS Y = 16 + 5 X.FIND THE EXPECTATION AND VARIANCE OF Y.E [Y] =VAR [Y] =1HOMEWORK 4 – STAT 3360 – FALL 2016DUE BY SEPTEMBER 29PLEASE, SUBMIT THIS DOCUMENT AND SHOW YOUR FIRST AND LAST NAME BELOW!STAPLE OR PAPERCLIP YOUR WORK, PLEASE!PROBLEM 2 [20 POINTS = 5 + 5 + 5 + 5]TWO RANDOM VARIABLES, X AND Y, ARE INDEPENDENT. THEIR MARGINALDISTRIBUTIONS ARE SPECIFIED AS FOLLOWS.– 1010%XPROBABILITYYPROBABILITY1.2.3.4.040%–470%550%630%FIND EXPECTATION FOR EACH VARIABLE.E [X] =E [Y] =FIND THE VARIANCE FOR EACH VARIABLE.VAR [X] =VAR [Y] =WHAT IS THE EXPECTATION OF THE NEW RANDOM VARIABLE, Z = 3X – 2Y?E [Z] =FIND THE VARIANCE OF Z (= 3X – 2Y).VAR [Z] =2HOMEWORK 4 – STAT 3360 – FALL 2016DUE BY SEPTEMBER 29PLEASE, SUBMIT THIS DOCUMENT AND SHOW YOUR FIRST AND LAST NAME BELOW!STAPLE OR PAPERCLIP YOUR WORK, PLEASE!PROBLEM 3 [50 POINTS = 10+15+15+10]SUZY IS A STOCK MARKET ANALYST. SHE WANTS TO BUILD A PORTFOLIO INVESTING50% INTO ONE STOCK AND 50% INTO THE OTHER. THREE STOCKS (I, II, AND III) ARECONSIDERED FOR SELECTION. THEIR EXPECTED ROI VALUES (IN CENTS PER DOLLAR)AND CORRESPONDING STANDARD DEVIATIONS (IN CENTS PER DOLLAR) ARE LISTED INTHE TABLE BELOW.STOCKROI EXPECTED ROI STANDARD DEVIATIONIX145IIY145IIIZ145IN ADDITION, SUZY ASSUMES THAT THE CORRELATION BETWEEN THE ROI FOR STOCK IAND THAT FOR STOCK II IS C [X, Y] = – 0.8, WHILE THE ROI FOR STOCK III ISUNCORRELATED WITH THAT FOR STOCK I (THAT IS C [Z, X] = 0). CORRELATIONBETWEEN THE ROI FOR STOCK II AND THAT FOR STOCK III WAS SET AS C [Y, Z] = 0.6.SHE WANTS TO MAKE A CHOICE BETWEEN TWO TYPES OF SCENARIO.FIRST SCENARIO OPERATES WITH STOCKS I AND II, SO THE ROI FOR THE PORTFOLIOWILL BE FOUND AS T = 0.5 X + 0.5 Y.THE ALTERNATIVE SCENARIO WILL OPERATE WITH STOCKS II AND III, SO THE ROI INTHIS CASE WILL BE W = 0.5 Y + 0.5 Z.HELP SUZY COMPARE TWO CHOICES FOR THE PORTFOLIO BY ANSWERING THEFOLLOWING QUESTIONS.1.2.WHAT IS THE EXPECTED ROI FOR T AND THAT FOR W?E [T] =E [W] =WHAT IS THE VOLATILITY (STANDARD DEVIATION) ASSOCIATED WITH THEPORTFOLIO CHARACTERIZED BY A RANDOM VARIABLE T?SD [T] =3.WHAT IS THE VOLATILITY (STANDARD DEVIATION) ASSOCIATED WITH THEPORTFOLIO CHARACTERIZED BY A RANDOM VARIABLE W?SD [W] =4.BASED ON VOLATILITY COMPARISON, WHICH SCENARIO (T OR W) WOULD YOURECOMMEND?3