Question

Problem 3. Plot the following binomial probability functions as a function of outcome (x) using EXCEL on the same graph, and then comment on the effect of the value of p. a. b(x;10,0.1) b. b(x;10,0.5) c. b(x;10,0.9)

Answer 1

x	p = 0.1	p = 0.5	p = 0.9
0	0.348678	0.000977	1E-10
1	0.38742	0.009766	9E-09
2	0.19371	0.043945	3.64E-07
3	0.057396	0.117188	8.75E-06
4	0.01116	0.205078	0.000138
5	0.001488	0.246094	0.001488
6	0.000138	0.205078	0.01116
7	8.75E-06	0.117188	0.057396
8	3.65E-07	0.043945	0.19371
9	9E-09	0.009766	0.38742
10	1E-10	0.000977	0.348678

This table contains the binomial probabilities for different values of "x". The plot of the three probability functions is given below.

We see that for p = 0.1, the distribution is positively skewed. For p = 0.5, the distribution is symmetric. For p = 0.9, the distribution is negatively skewed. This tells us that as p approaches the value of 0.5, the distribution becomes symmetric and as we move away from 0.5, the distribution becomes skewed.