Extra\tCredit\tAssignment\tBefore\tMidterm\tExam\t#2 Due\tWednesday\tMarch\t30,\t2016 1.\tA\tnew\ttype\tof\tnail\tgun\tfires\tnails\tinto\twooden\tblocks\tat\ta\tmean\tvelocity\tof\t2000 miles\tper\thour.\tThe\tpdf\tof\tthe\tvelocity\thas\tthe\tform c(v 1000)(3000 v) for 1000 < v < 3000 f (v) = 0 otherwise a)\t(1\tpoint)\tWhat\tis\tthe\tvalue\tof\tc? b)\t(2\tpoints)\tWhat\tis\tthe\tvariance\tof\tthe\tvelocity? c)\t(2\tpoints)\tThe\tkenetic\tenergy,\tX,\tassociated\twith\ta\tmass\tm\tmoving\tat\tvelocity\tV\tis given\tby X=mV2/2. Find\tthe\texpected\tkenetic\tenergy\tassociated\twith\ta\tnail\tof\tmass\tm\tfired from\tthe\tnail\tgun. 2. (6 points - 1 point each) For each situation below, specify which distributional model would be most appropriate for the random variable X (5 points each). a) Twenty students apply for a summer internship, out of which ten are in their senior year. Six students are randomly selected for interviews. Let X = how many seniors are interviewed. b) Let X = how many cars pass you on the highway before one of them is silver colored c) Let X = how long in minutes until the next 2001 Toyota Prius hybrid goes through a toll booth on the Golden Gate Bridge d) When you wake up tomorrow morning you look at the digital clock next to your bed and watch it until the time changes (i.e. until it changes to the next minute). Let X = how long you have to wait in minutes. e) The marginal distribution of X whose joint distribution with Y is given by f(x,y) = 27x2e-3x-2y for 0