Many thanks 2. The UWI campus is located in an area with the highest lightning s
ID: 3339748 • Letter: M
Question
Many thanks 2. The UWI campus is located in an area with the highest lightning struck in the rainy season. As the IT and Learning Facilities manager in UWI, Tito's main duty is to maintain the facilities in the campus so that ali the activities, especially the teaching and learning activities in class goes well. Tito's past experience show that on the average, 1 computer in 800 crashes during a severe thunderstorm. One day, a storm struck, and UWI had 4,000 working computers on the day when the area was hit by a severe thunderstorm. Questions, assuming that it follows Poisson distribution: How many computers should Tito expect to crash on that day? Calculate also the variance of computers crashed.(5 points) a. b. c. Compute the probability that less than 10 computers crashed.(10 points) Compute the probability that exactly 10 computers crashed.(5 points)Explanation / Answer
Part a
Mean for Poisson distribution is given as 1 for 800 computers.
For 16000 computers, mean = (1/800)*16000 = 0.00125*16000 = 20
About 20 computers should Tito expect to crash on that day.
We know that mean and variance for Poisson distribution are same.
Mean = Variance =
So, variance of computers crashed is 20.
Part b
We have to find P(X<10)
P(X<10) = P(X9) = P(X=0) + P(X=1) + .....+P(X=9)
P(X=x) = ^x*exp(-)/x!
= 20
Probabilities are calculated as below:
X
P(X)
0
20^0*exp(-20)/0! = 0.000000002
1
20^1*exp(-20)/1! = 0.000000041
2
20^2*exp(-20)/2! = 0.000000412
3
20^3*exp(-20)/3! = 0.000002748
4
20^4*exp(-20)/4! = 0.000013741
5
20^5*exp(-20)/5! = 0.000054964
6
20^6*exp(-20)/6! = 0.000183214
7
20^7*exp(-20)/7! = 0.000523468
8
20^8*exp(-20)/8! = 0.001308669
9
20^9*exp(-20)/9! = 0.002908153
Total
0.004995412
Required probability = 0.004995412
Part c
Here, we have to find P(X=10)
P(X=x) = ^x*exp(-)/x!
P(X=10) = 20^10*exp(-20)/10! =0.005816307
Required probability = 0.005816307
X
P(X)
0
20^0*exp(-20)/0! = 0.000000002
1
20^1*exp(-20)/1! = 0.000000041
2
20^2*exp(-20)/2! = 0.000000412
3
20^3*exp(-20)/3! = 0.000002748
4
20^4*exp(-20)/4! = 0.000013741
5
20^5*exp(-20)/5! = 0.000054964
6
20^6*exp(-20)/6! = 0.000183214
7
20^7*exp(-20)/7! = 0.000523468
8
20^8*exp(-20)/8! = 0.001308669
9
20^9*exp(-20)/9! = 0.002908153
Total
0.004995412