Question

A call center recieves an average of 10 calls per hour. Assuming the number of calls received follows the poisson distribution, determine the probability of each of the discrete outcomes below. Then calculate the variance component for each one using the standard formula for the variance of a discrete random variable. At the end, take the sum of both columns.

What excel formula is used to calculate the variance component for each one using the standard formula for the variance of a discrete random variable?

Poisson Distribution Table
Calls	Density	Variance
0	0.00%
1	0.05%
2	0.23%
3	0.76%
4	1.89%
5	3.78%
6	6.31%
7	9.01%
8	11.26%
9	12.51%
10	12.51%
11	11.37%
12	9.48%
13	7.29%
14	5.21%
15	3.47%
16	2.17%
17	1.28%
18	0.71%
19	0.37%
20	0.19%
21	0.09%
22	0.04%
23	0.02%
24	0.01%
25	0.00%
26	0.00%
27	0.00%
28	0.00%
29	0.00%
30	0.00%
Sum	100.00%

Answer 1

Calls	Density	np	n^2* p
0	0.00%	0.00%	0
1	0.05%	0.05%	0.0005
2	0.23%	0.46%	0.0092
3	0.76%	2.28%	0.0684
4	1.89%	7.56%	0.3024
5	3.78%	18.90%	0.945
6	6.31%	37.86%	2.2716
7	9.01%	63.07%	4.4149
8	11.26%	90.08%	7.2064
9	12.51%	112.59%	10.1331
10	12.51%	125.10%	12.51
11	11.37%	125.07%	13.7577
12	9.48%	113.76%	13.6512
13	7.29%	94.77%	12.3201
14	5.21%	72.94%	10.2116
15	3.47%	52.05%	7.8075
16	2.17%	34.72%	5.5552
17	1.28%	21.76%	3.6992
18	0.71%	12.78%	2.3004
19	0.37%	7.03%	1.3357
20	0.19%	3.80%	0.76
21	0.09%	1.89%	0.3969
22	0.04%	0.88%	0.1936
23	0.02%	0.46%	0.1058
24	0.01%	0.24%	0.0576
25	0.00%	0.00%	0
26	0.00%	0.00%	0
27	0.00%	0.00%	0
28	0.00%	0.00%	0
29	0.00%	0.00%	0
30	0.00%	0.00%	0
Sum	100.00%	1000.10%	11001.40%

variance = E(X^2) - (E(X))^2

= 110.014 - 10.001^2

=9.993999