Question

. Consider Beta pdf and plot it on the same paper for various values of
alpha and beta: alpha = 1,2,3,4,5 and beta=1/2, 1, 3/2, 2, 5/2. Considr
all combinations.

2. Consider gamma pdf and plot it on the same paper for various values of
alpha and beta: alpha = 1/2, 1, 3/2, 2, 5/2 and beta = 1, 2, 3, 4, 5.
Consider all possible combinations.

3. Consider Normal pdf and plot it on the same apper for various values of
mu and sigma: mu=0, -1, 1, -2, 2 and sigma = 1, 2, 3, 4, 5. Consider all
possible combinatioons.

Use excel

Answer 1

1. Using excel, we can use the BETA.DIST function to calculate the values of probability distribution for different combinations and plot the graph. The data collected is:

Alpha	1.000	2.000	3.000	4.000	5.000
Beta	0.500	1.000	1.500	2.000	2.500
Xi	Y1	Y2	Y3	Y4	Y5
0.001	0.500	0.002	0.000	0.000	0.000
0.100	0.527	0.200	0.062	0.018	0.005
0.200	0.559	0.400	0.235	0.128	0.067
0.300	0.598	0.600	0.494	0.378	0.278
0.400	0.645	0.800	0.813	0.768	0.698
0.500	0.707	1.000	1.160	1.250	1.296
0.600	0.791	1.200	1.494	1.728	1.923
0.700	0.913	1.400	1.761	2.058	2.314
0.800	1.118	1.600	1.878	2.048	2.149
0.900	1.581	1.800	1.681	1.458	1.217
0.950	2.236	1.900	1.324	0.857	0.534

2. For gamma distribution, we can use the following formula in excel: GAMMA.DIST

The graph is:

3. For normal distribution, we will use the formula NORM.DIST.

The data used is:

Mu	0.000	-1.000	1.000	-2.000	2.000
Sigma	1.000	2.000	3.000	4.000	5.000
Xi	Y1	Y2	Y3	Y4	Y5
-10.000	0.000	0.000	0.000	0.013	0.004
-8.000	0.000	0.000	0.001	0.032	0.011
-6.000	0.000	0.009	0.009	0.060	0.022
-4.000	0.000	0.065	0.033	0.088	0.039
-2.000	0.054	0.176	0.081	0.100	0.058
0.000	0.399	0.176	0.126	0.088	0.074
2.000	0.054	0.065	0.126	0.060	0.080
4.000	0.000	0.009	0.081	0.032	0.074
6.000	0.000	0.000	0.033	0.013	0.058
8.000	0.000	0.000	0.009	0.004	0.039
10.000	0.000	0.000	0.001	0.001	0.022