Question

A random sample of size 30 from an exponential distribution with mean 5 is simulated.

Describe the process of plotting the empirical cdf for this sample along with the true cdf in the sample graph.

Answer 1

We have calculated pdf and cdf of exponential with mean 5,

for plotting steps

1)

we draw 30 samples from pdf

2)

then for these 30 samples we draw find CDF of those 30 corresponding samples,

3)

then we plot PDF and CDF on same graph taking x axis as 1:30

plot is

The PDF and CDF plot of exponential distribution with mean 5 PDF CDF 10 15 20 25 30 1:30

random samples are

Observation	PDF	CDF
1	5.446	0.664
2	4.31	0.578
3	2.646	0.411
4	9.489	0.85
5	9.636	0.854
6	6.771	0.742
7	2.227	0.359
8	9.852	0.861
9	2.997	0.451
10	0.017	0.003
11	0.595	0.112
12	1.538	0.265
13	6.73	0.74
14	9.365	0.846
15	4.489	0.593
16	2.948	0.445
17	1.57	0.269
18	1.894	0.315
19	3.394	0.493
20	1.215	0.216
21	1.311	0.231
22	5.001	0.632
23	4.177	0.566
24	1.373	0.24
25	2.462	0.389
26	9.11	0.838
27	5.547	0.67
28	2.945	0.445
29	5.338	0.656
30	6.285	0.716