Question

Given the probability distributions shown to the right, complete the following parts. a. Compute the expected value for each distribution. b. Compute the standard deviation for each distribution. c. What is the probability that x will be at least 3 in Distribution A and Distribution B? d. Compare the results of distributions A and B.		Distribution A		Distribution B
		x Subscript ixi	P(Xequals=x Subscript ixi )	x Subscript ixi	P(Xequals=x Subscript ixi )
		0	0.480.48	0	0.050.05
		1	0.240.24	1	0.090.09
		2	0.140.14	2	0.140.14
		3	0.090.09	3	0.240.24
		4	0.050.05	4

Answer 1

a) Expected value of A E(A)= x*p(x)= 0*0.48+1*0.24+2*0.14+3*0.09+4*0.05= 0.99

E(B) = (0*0.05+1*0.09+2*0.14+3*0.24)= 1.09

b) V(A)= E(A^2)+{E(A)}^2

E(A^2)= = (0)^2*0.48 +(1)^2*0.24 +(2)^2*0.14+(3)^2*0.09+(4)^2*(0.05) =2.41

V(A)= 2.41-(0.99)^2

V(A)= 2.41-0.98

V(A)=1.43

STD (A)= SQRT(1.43)= 1.196

V(B)= E(B^2)+{E(B)}^2

E(B^2)= = (0)^2*0.05 +(1)^2*0.09 +(2)^2*0.14+(3)^2*0.24= 2.81

V(B)= 2.81-(1.09)^2= 2.81-1.19= 1.62

STD(B)= SQRT(1.62)= 1.27

c) In A distribution P(X>=3)= 0.09+0.05= 0.14

In B distribution P(X>=3)=0.24

THERE IS MORE VARIABILITY IN DISTRIBUTION B THAN IN A