nt due Nov 18 15 points Extra Credit Assignment due November

nt (due Nov 18) 15 points Extra Credit Assignment due November 18, 2016 1. (5 points. The number of cars that pull into a rest area on a busy road averages about one per minute independently all day long. a) (2 point) Let X- how many cars will go into the rest area in the next 5 minutes. What is the pmfofX? What assumptions are you making? b) (1 points0 Let Y- how long it will be before 7 cars pull into the rest area. What is the variance of Y? c) (2 points) Assuming 5 cars come into the rest area in the next 10 minutes, what is the pdf of the time that the third car will arrive? 2. (5 points)X and Y have a joint density of the form f(xy) c(1-y) for 0sxsysi 0 otherwise) a) (1 point) what is the value of c? b) (1 point) Are Xand Y independent? Explain briefly how you know. c) (1 point) Find the marginal pdf ofX. d) (2 points) Find the conditional pdf of X given that Y-0.75. 3. (5 points) a) (2 points) When you observe three independent variables that each follow the Uniform distribution between 0 and 1; what is the pdf of their median? MacBook Air

Solution

rest area are typically noncommercial facilities tha provide at a minimum,parking and restroomsome may haveinformation kiosksand picnic areabut little else while some havedump facilities where recreationalvehicles may empty their sewageholiding tanks they are mantaned by departement of transport

a. in next 5 min. there is 5 cars to park in rest area

b. valancy ofY is 2

c. 6 min