Question

11. using the probability listed below

x 0 1 2 3 4

p(x) 0.10 0.26 0.30 0.24 0.10

a. find the mean, variance and standard deviation

b. find p(x is no more than 3)

c. find p(x is at least 2)

d. find p(x<2 or x >2)

e. find p(x is less than 3)

Answer 1

11)

Solution :

x	P(x)	x * P(x)	x2 * P(x)
0	0.1	0	0
1	0.26	0.26	0.26
2	0.3	0.6	1.2
3	0.24	0.72	2.16
4	0.1	0.4	1.6
Sum	1	1.98	5.22

(a)

Mean = = X * P(X) = 1.98

variance =  X ² * P(X) - ² = 5.22 - 1.98² = 1.2996

Standard deviation = = 1.14

(b)

P(x is no more than 3) = 0.10 + 0.26 + 0.30 + 0.24 = 0.90

(c)

(x is at least 2) = 0.30 + 0.24 + 0.10 = 0.64

(d)

(x<2 or x >2) = 0.10 + 0.26 + 0.24 + 0.10 = 0.70

(e)

(x is less than 3) = 0.10 + 0.26 + 0.30 = 0.66