Patients arrive to an emergency hospital unit according to a Poisson pro- cess with parameter > 0. They are assisted on a first arrived first assisted basis. Patients are assisted one by one.

i) Estimate the parameter based on data in file patients k(contained in the folder ) posted on D2L. Each observation represents the number of daily patients arrived to the emergency hospital.

ii) Find the probability that no arrivals occur in an interval of 5 hours.

iii) Find the probability that at least one arrival occurs in a day.

iv) What is the estimated mean and the variance of the number of ar- rivals during a day?

v) The time a single patients takes to be completely assisted has a ran- dom probability distribution with exponential distribution of param- eter = 30 min/patient. Find the average and the standard devia- tion of the total time patients have been assisted during a day. Find the p.d.f. of the total time.

1-3-21	4
2-3-21	4
3-3-21	4
4-3-21	3
5-3-21	6
6-3-21	2
7-3-21	5
8-3-21	2
9-3-21	4
10-3-21	4
11-3-21	2
12-3-21	5
13-3-21	2
14-3-21	5
15-3-21	7
16-3-21	4
17-3-21	3
18-3-21	7
19-3-21	5
20-3-21	0
21-3-21	4
22-3-21	5
23-3-21	6
24-3-21	4
25-3-21	3
26-3-21	4
27-3-21	3
28-3-21	4
29-3-21	0
30-3-21	2
31-3-21	5
1-4-21	5
2-4-21	2
3-4-21	2
4-4-21	3
5-4-21	2
6-4-21	2
7-4-21	5
8-4-21	2
9-4-21	4
10-4-21	1
11-4-21	7
12-4-21	2
13-4-21	3
14-4-21	3
15-4-21	0
16-4-21	3
17-4-21	3
18-4-21	3
19-4-21	4
20-4-21	6
21-4-21	4
22-4-21	1
23-4-21	3
24-4-21	0
25-4-21	2
26-4-21	4
27-4-21	6
28-4-21	3
29-4-21	2
30-4-21	2
1-5-21	5
2-5-21	2
3-5-21	1
4-5-21	3
5-5-21	2
6-5-21	4
7-5-21	2
8-5-21	3
9-5-21	3
10-5-21	2
11-5-21	3
12-5-21	3
13-5-21	2
14-5-21	2
15-5-21	2
16-5-21	2
17-5-21	3
18-5-21	4
19-5-21	4
20-5-21	3
21-5-21	5
22-5-21	2
23-5-21	0
24-5-21	4
25-5-21	1
26-5-21	2
27-5-21	4
28-5-21	2
29-5-21	3
30-5-21	1
31-5-21	2
1-6-21	3
2-6-21	3
3-6-21	5
4-6-21	4
5-6-21	3
6-6-21	0
7-6-21	3
8-6-21	3