From previous experiments (Aka, a lone Saturday spent in Krannert and seeing exactly 3 students in an hour –
Liz, Christine, and Brad to be exact) we conclude that “on average” we will see 3 fellow stat 225 students per
hour. If X is the number of students we see an hour:
Distribution/Parameters: Poisson(λ1 hour=3)
On this particular Saturday, Danny Porter decides he wants to shoot/edit some film –He’s a busy guy, so he was
only there from 12:30 – 1:00. Little did he know it would be such an EXCITING day outside of Krannert. David
and Jim had a mini golfing tournament trying to drive the ball over the Union dodging innocent cars driving by
while Jared practiced his lacrosse moves before Matt DeSilva ran by so quickly it’s a good thing Danny was
ready with the camera. What is the probability that he would have seen 4 fellow classmates in the 30 minutes
he was filming?
λ.5 hours = 1.5 P(X=4) = e^-1.5*1.5^4/4!
Soo Yun hears of the excitement going on outside of Krannert, so she decides to sit down with some music and
coffee for 2 hours to see what happens. What is the probability that in 2 hours, she sees less fellow stat 225
students than Danny did in 30 minutes?
λ2 hours =6 - P(X<4) = P(X=0)+P(X=1)+P(X=2)+P(X=3)= e^6(6^0/0!+6^1/1!+6^2/2!+6^3/3!)
Matt Daily, Rob Bond, Jason Koke and Chris Moorman were all huddled around excited for the start of a new
baseball season! Cory, their fellow classmate and EXCELLENT chef was elected to bring lunch. So far they have
been waiting for an hour – they were so engrossed in their excitement they didn’t realize how hungry they
were… but in another 15 minutes their stomachs are going to get their complete attention and they are not
going to be happy. What is the probability that Cory gets there before his fellow classmates lose their
patience?
P(X<1 hour 15 min| X>1 hour) = P(X<15 min) = 1-e^-3*(1/4)
Chris Miller decides this is a perfect time to practice his stage antics and is awesome guitar tricks… what is the
probability that Josh just happens to come around with his guitar 5 to 10 minutes later and then Charlie joins in
the jam session before half an hour goes by?
P(5<X<10)*P(X<30) = [(1-e^-3*(1/6))-(1-e^-3*(1/12))]*(1-e^-3*(1/2))
How long should we have EXPECTED Chris to wait before any band members joined him?
E(X) = 1/3 = 20 minutes
Andrew decides to test his probability skills, after practicing some vocals with the little rock band. Chris, Josh
and Charlie finish up, and Andrew waits for 45 minutes and sees exactly 4 other students, Joe and Bill decided
to take a break from some Saturday reading and walked by and a Mike Lubrano and Mike Malstrom overshot
the football and had to pass by. Knowing that there were exactly 4 students in this 45 minute period, what’s the
probability that ALL of them arrived in the last 5?
P(40<X<45)^4 = (45-40/45-0)^4 = (1/9)^4
From previous - “on average” we will see 3 fellow stat 225 students per hour.
Distribution/Parameters: Poisson(λ1 hour=3)
Danny Porter shoot/edit some film 12:30 – 1:00
David and Jim had a mini golfing tournament
Jared practiced his lacrosse moves
Matt DeSilva ran by so quickly it’s a good thing Danny was ready with the camera.
What is the probability that he would have seen 4 fellow classmates in the 30 minutes he was filming?
λ.5 hours = 1.5 P(X=4) = e^-1.5*1.5^4/4!
Soo Yun 2 hours to see what happens.
What is the probability that in 2 hours, she sees less fellow stat 225 students than Danny did in 30 minutes?
λ2 hours =6 - P(X<4) = P(X=0)+P(X=1)+P(X=2)+P(X=3)= e^6(6^0/0!+6^1/1!+6^2/2!+6^3/3!)
Matt Daily, Rob Bond, Jason Koke and Chris Moorman baseball season!
Cory, next Emeril – bring lunch
So far they have been waiting for an hour –in another 15 minutes
What is the probability that Cory gets there before his fellow classmates lose their patience?
P(X<1 hour 15 min| X>1 hour) = P(X<15 min) = 1-e^-3*(1/4)
Chris Miller is awesome guitar tricks…
Josh just happens to come around with his guitar 5 to 10 minutes later and then
Charlie joins in the jam session within half an hour?
P(5<X<10)*P(X<30) = [(1-e^-3*(1/6))-(1-e^-3*(1/12))]*(1-e^-3*(1/2))
How long should we have EXPECTED Chris to wait before any band members joined him?
E(X) = 1/3 = 20 minutes
Andrew after practicing some vocals 45 minutes and sees exactly 4 other students,
Joe and Bill decided to take a break from some Saturday reading
Off to tell Haley of some exciting Irish books
Mike Lubrano (fellow East Coaster) and Mike Malstrom overshot the football
4 students in this 45 minute period, ALL of them arrived in the last 5 minutes?
P(40<X<45)^4 = (45-40/45-0)^4 = (1/9)^4