Question

Q 418. Using an LCG generator with parameters a: 21, m: 100, c: 13 and x0: 7 generate (if possible) a random variate from each of the following distributions. For each sub question, you may restart the LCG stream (i.e. feel free to reuse the same random number for each sub-question)

a. Normal (15, 5)

b. Gamma (5, 4)

c. Poisson (2)

d. Weibull (2, 2)

e.Triangular(1,2,5)                                                                                

Answer 1

	Table 1 : Randon number sequence for Linear Congruential Generator
	Start Seed X0 = 7
	Parameters					Sequence of Random numbers
S.no.	a	Xn	C	m	((a*Xn)+c)	Xn+1 = ((a*xn)+c)mod(m)
1	21	7	13	100	160	60
2	21	60	13	100	1273	73
3	21	73	13	100	1546	46
4	21	46	13	100	979	79
5	21	79	13	100	1672	72
6	21	72	13	100	1525	25
7	21	25	13	100	538	38
8	21	38	13	100	811	11
9	21	11	13	100	244	44
10	21	44	13	100	937	37
11	21	37	13	100	790	90
12	21	90	13	100	1903	3
13	21	3	13	100	76	76
14	21	76	13	100	1609	9
15	21	9	13	100	202	2
16	21	2	13	100	55	55
17	21	55	13	100	1168	68
18	21	68	13	100	1441	41
19	21	41	13	100	874	74
20	21	74	13	100	1567	67
21	21	67	13	100	1420	20
22	21	20	13	100	433	33
23	21	33	13	100	706	6
24	21	6	13	100	139	39
25	21	39	13	100	832	32
26	21	32	13	100	685	85
27	21	85	13	100	1798	98
28	21	98	13	100	2071	71
29	21	71	13	100	1504	4
30	21	4	13	100	97	97

Table 2. Random number variates for given distributions
					a. Normal (15,5)	b. Gamma(5,4)	c. poisson(2)	d. Weibull(2,2)
Xn=x	a	b	y=ax+b		NORMAL(15,5)	Gamma(5,4)	Poisson(2)	Weibull(2,2)
60	15	5	905		1	0.999143359	1	1
73	15	5	1100		1	0.999930957	1	1
46	15	5	695		1	0.989253422	1	1
79	15	5	1190		1	0.999979253	1	1
72	15	5	1085		1	0.999915824	1	1
25	15	5	380		0.977249868	0.747014677	1	1
38	15	5	575		0.999997888	0.959737318	1	1
11	15	5	170		0.211855399	0.144621488	0.999998635	1
44	15	5	665		0.999999997	0.984895399	1	1
37	15	5	560		0.999994587	0.952907277	1	1
90	15	5	1355		1	0.999997825	1	1
3	15	5	50		0.008197536	0.001064678	0.85712346	0.894600775
76	15	5	1145		1	0.999962048	1	1
9	15	5	140		0.11506967	0.078014105	0.999953502	0.999999998
2	15	5	35		0.004661188	0.000172116	0.676676416	0.632120559
55	15	5	830		1	0.997830523	1	1
68	15	5	1025		1	0.999815302	1	1
41	15	5	620		0.9999999	0.975137134	1	1
74	15	5	1115		1	0.999943407	1	1
67	15	5	1010		1	0.999775617	1	1
20	15	5	305		0.841344746	0.559506715	1	1
33	15	5	500		0.999840891	0.913813889	1	1
6	15	5	95		0.035930319	0.018575936	0.995466194	0.99987659
39	15	5	590		0.999999207	0.965647279	1	1
32	15	5	485		0.999663071	0.900367599	1	1
85	15	5	1280		1	0.999993892	1	1
98	15	5	1475		1	0.999999593	1	1
71	15	5	1070		1	0.999897443	1	1
4	15	5	65		0.013903448	0.003659847	0.947346983	0.981684361
97	15	5	1460		1	0.999999497	1	1