Question

1. For the given random process of the total number of visitors that visit a museum per hour, find the followings: 1415 p(x)0.150.120.110.20.080.090.080.050.12 2 10 12 a) Mean, variance, and standard deviation. b) The probability that the total number of visitors not exceed 3 visitors. c) The probability that the total number of visitors not less than 9 visitors

Answer 1

(a) mean=E(x)=sum(x*p(x))=7.2 ,

variance=E(x²)-E(x)*E(x)=76.98-7.2*7.2=25.14

standard deviation=sqrt(vaiance)=sqrt(25.14)=5.014

x	p(x)	x*p(x)	x2*p(x)
1	0.15	0.15	0.15
2	0.12	0.24	0.48
5	0.11	0.55	2.75
7	0.2	1.4	9.8
9	0.08	0.72	6.48
10	0.09	0.9	9
12	0.08	0.96	11.52
14	0.05	0.7	9.8
15	0.12	1.8	27
sum=	1	7.42	76.98

(b) P(not exceed 3)=P(X=1)+P(x=2)=0.15+0.12=0.27

(c)P(not less than 9)=P(X=10)+P(X=12)+P(X=14)+P(X=15)=0.09+0.08+0.05+0.12=0.34